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class
aeif_cond_alpha
: public Archiving_Node  #include <aeif_cond_alpha.h>
Name: aeif_cond_alpha  Conductance based exponential integrateandfire neuron model according to Brette and Gerstner (2005). Description:
aeif_cond_alpha is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005). Synaptic conductances are modelled as alphafunctions.
This implementation uses the embedded 4th order RungeKuttaFehlberg solver with adaptive step size to integrate the differential equation.
The membrane potential is given by the following differential equation:
\[\begin{split} C_m \frac{dV}{dt} = g_L(VE_L)+g_L\Delta_T\exp\left(\frac{VV_{th}}{\Delta_T}\right)  g_e(t)(VE_e) \\ g_i(t)(VE_i)w +I_e \end{split}\]and
\[ \tau_w \frac{dw}{dt} = a(VE_L)  w \]Parameters:
The following parameters can be set in the status dictionary.
Dynamic state variables:
V_m
mV
Membrane potential
g_ex
nS
Excitatory synaptic conductance
dg_ex
nS/ms
First derivative of g_ex
g_in
nS
Inhibitory synaptic conductance
dg_in
nS/ms
First derivative of g_in
w
pA
Spikeadaptation current
Membrane Parameters
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_reset
mV
Reset value for V_m after a spike
E_L
mV
Leak reversal potential
g_L
nS
Leak conductance
I_e
pA
Constant external input current
Spike adaptation parameters
a
ns
Subthreshold adaptation
b
pA
Spiketriggered adaptation
Delta_T
mV
Slope factor
tau_w
ms
Adaptation time constant
V_th
mV
Spike initiation threshold
V_peak
mV
Spike detection threshold
Synaptic parameters
E_ex
mV
Excitatory reversal potential
tau_syn_ex
ms
Rise time of excitatory synaptic conductance (alpha function)
E_in
mV
Inhibitory reversal potential
tau_syn_in
ms
Rise time of the inhibitory synaptic conductance (alpha function)
Integration parameters
gsl_error_tol
real
This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.
Authors: MarcOliver Gewaltig; full revision by Tanguy Fardet on December 2016
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
References:
 1
Brette R and Gerstner W (2005). Adaptive Exponential IntegrateandFire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:36373642 DOI: https://doi.org/10.1152/jn.00686.2005
SeeAlso: iaf_cond_alpha, aeif_cond_exp

class
aeif_cond_alpha_multisynapse
: public Archiving_Node  #include <aeif_cond_alpha_multisynapse.h>
Name: aeif_cond_alpha_multisynapse  Conductance based adaptive exponential integrateandfire neuron model according to Brette and Gerstner (2005) with multiple synaptic rise time and decay time constants, and synaptic conductance modeled by an alpha function.
Description:
aeif_cond_alpha_multisynapse is a conductancebased adaptive exponential integrateandfire neuron model. It allows an arbitrary number of synaptic time constants. Synaptic conductance is modeled by an alpha function, as described by A. Roth and M.C.W. van Rossum in Computational Modeling Methods for Neuroscientists, MIT Press 2013, Chapter 6.
The time constants are supplied by an array, “tau_syn”, and the pertaining synaptic reversal potentials are supplied by the array “E_rev”. Port numbers are automatically assigned in the range from 1 to n_receptors. During connection, the ports are selected with the property “receptor_type”.
The membrane potential is given by the following differential equation:
\[ C dV/dt = g_L(VE_L) + g_L*\Delta_T*\exp((VV_T)/\Delta_T) + I_{syn_{tot}}(V, t) w + I_e \]where\[ I_{syn_{tot}}(V,t) = \sum_i g_i(t) (V  E_{rev,i}) , \]the synapse i is excitatory or inhibitory depending on the value of \( E_{rev,i}\) and the differential equation for the spikeadaptation current w is:
\[ \tau_w * dw/dt = a(V  E_L)  w \]When the neuron fires a spike, the adaptation current w < w + b.
Parameters:
The following parameters can be set in the status dictionary.
Dynamic state variables:
V_m
mV
Membrane potential
w
pA
Spikeadaptation current
Membrane Parameters
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_reset
mV
Reset value for V_m after a spike
E_L
mV
Leak reversal potential
g_L
nS
Leak conductance
I_e
pA
Constant external input current
Delta_T
mV
Slope factor
V_th
mV
Spike initiation threshold
V_peak
mV
Spike detection threshold
Spike adaptation parameters
a
ns
Subthreshold adaptation
b
pA
Spiketriggered adaptation
tau_w
ms
Adaptation time constant
Synaptic parameters
E_rev
list of mV
Reversal potential
tau_syn
list of ms
Time constant of synaptic conductance
Integration parameters
gsl_error_tol
real
This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.
Examples:
import nest import numpy as np neuron = nest.Create('aeif_cond_alpha_multisynapse') nest.SetStatus(neuron, {"V_peak": 0.0, "a": 4.0, "b":80.5}) nest.SetStatus(neuron, {'E_rev':[0.0, 0.0, 0.0, 85.0], 'tau_syn':[1.0, 5.0, 10.0, 8.0]}) spike = nest.Create('spike_generator', params = {'spike_times': np.array([10.0])}) voltmeter = nest.Create('voltmeter', 1, {'withgid': True}) delays=[1.0, 300.0, 500.0, 700.0] w=[1.0, 1.0, 1.0, 1.0] for syn in range(4): nest.Connect(spike, neuron, syn_spec={'model': 'static_synapse', 'receptor_type': 1 + syn, 'weight': w[syn], 'delay': delays[syn]}) nest.Connect(voltmeter, neuron) nest.Simulate(1000.0) dmm = nest.GetStatus(voltmeter)[0] Vms = dmm["events"]["V_m"] ts = dmm["events"]["times"] import pylab pylab.figure(2) pylab.plot(ts, Vms) pylab.show()
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Author: Hans Ekkehard Plesser, based on aeif_cond_beta_multisynapse
SeeAlso: aeif_cond_alpha_multisynapse

class
aeif_cond_alpha_RK5
: public Archiving_Node  #include <aeif_cond_alpha_RK5.h>
Name: aeif_cond_alpha_RK5  Conductance based exponential integrateandfire neuron model according to Brette and Gerstner (2005)
Description:
aeif_cond_alpha_RK5 is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005). Synaptic conductances are modelled as alphafunctions.
This implementation uses a 5th order RungeKutta solver with adaptive stepsize to integrate the differential equation (see Numerical Recipes 3rd Edition, Press et al. 2007, Ch. 17.2).
The membrane potential is given by the following differential equation:
\[\begin{split} C dV/dt= g_L(VE_L)+g_L*\Delta_T*\exp((VV_T)/\Delta_T)g_e(t)(VE_e) \\ g_i(t)(VE_i)w +I_e \end{split}\]and\[ \tau_w * dw/dt= a(VE_L) w \]Parameters:
The following parameters can be set in the status dictionary.
Dynamic state variables:
V_m
mV
Membrane potential
g_ex
nS
Excitatory synaptic conductance
dg_ex
nS/ms
First derivative of g_ex
g_in
nS
Inhibitory synaptic conductance
dg_in
nS/ms
First derivative of g_in
w
pA
Spikeadaptation current
Membrane Parameters
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_reset
mV
Reset value for V_m after a spike
E_L
mV
Leak reversal potential
g_L
nS
Leak conductance
I_e
pA
Constant external input current
Spike adaptation parameters
a
ns
Subthreshold adaptation
b
pA
Spiketriggered adaptation
Delta_T
mV
Slope factor
tau_w
ms
Adaptation time constant
V_th
mV
Spike initiation threshold
V_peak
mV
Spike detection threshold
Synaptic parameters
E_ex
mV
Excitatory reversal potential
tau_syn_ex
ms
Rise time of excitatory synaptic conductance (alpha function)
E_in
mV
Inhibitory reversal potential
tau_syn_in
ms
Rise time of the inhibitory synaptic conductance (alpha function)
Numerical integration parameters
HMIN
ms
Minimal stepsize for numerical integration (default 0.001ms)
MAXERR
mV
Error estimate tolerance for adaptive stepsize control (steps accepted if err<=MAXERR). Note that the error refers to the difference between the 4th and 5th order RK terms. Default 1e10 mV.
Authors: Stefan Bucher, MarcOliver Gewaltig.
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
 1
Brette R and Gerstner W (2005). Adaptive Exponential IntegrateandFire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:36373642. DOI: https://doi.org/10.1152/jn.00686.2005
SeeAlso: iaf_cond_alpha, aeif_cond_exp, aeif_cond_alpha

class
aeif_cond_beta_multisynapse
: public Archiving_Node  #include <aeif_cond_beta_multisynapse.h>
Name: aeif_cond_beta_multisynapse  Conductance based adaptive exponential integrateandfire neuron model according to Brette and Gerstner (2005) with multiple synaptic rise time and decay time constants, and synaptic conductance modeled by a beta function.
Description:
aeif_cond_beta_multisynapse is a conductancebased adaptive exponential integrateandfire neuron model. It allows an arbitrary number of synaptic rise time and decay time constants. Synaptic conductance is modeled by a beta function, as described by A. Roth and M.C.W. van Rossum in Computational Modeling Methods for Neuroscientists, MIT Press 2013, Chapter 6.
The time constants are supplied by two arrays, “tau_rise” and “tau_decay” for the synaptic rise time and decay time, respectively. The synaptic reversal potentials are supplied by the array “E_rev”. The port numbers are automatically assigned in the range from 1 to n_receptors. During connection, the ports are selected with the property “receptor_type”.
The membrane potential is given by the following differential equation:
\[ C dV/dt = g_L(VE_L) + g_L*\Delta_T*\exp((VV_T)/\Delta_T) + I_{syn_{tot}}(V, t)  w + I_e \]where:
\[ I_{syn_{tot}}(V,t) = \sum_i g_i(t) (V  E_{rev,i}) , \]the synapse i is excitatory or inhibitory depending on the value of \( E_{rev,i} \) and the differential equation for the spikeadaptation current w is:
\[ \tau_w * dw/dt = a(V  E_L)  w \]When the neuron fires a spike, the adaptation current w < w + b.
Parameters: The following parameters can be set in the status dictionary.
Dynamic state variables:
V_m
mV
Membrane potential
w
pA
Spikeadaptation current
Membrane Parameters
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_reset
mV
Reset value for V_m after a spike
E_L
mV
Leak reversal potential
g_L
nS
Leak conductance
I_e
pA
Constant external input current
Delta_T
mV
Slope factor
V_th
mV
Spike initiation threshold
V_peak
mV
Spike detection threshold
Spike adaptation parameters
a
ns
Subthreshold adaptation
b
pA
Spiketriggered adaptation
tau_w
ms
Adaptation time constant
Synaptic parameters
E_rev
list of mV
Reversal potential
tau_syn
list of ms
Time constant of synaptic conductance
Integration parameters
gsl_error_tol
real
This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.
Examples:
import nest import numpy as np neuron = nest.Create('aeif_cond_beta_multisynapse') nest.SetStatus(neuron, {"V_peak": 0.0, "a": 4.0, "b":80.5}) nest.SetStatus(neuron, {'E_rev':[0.0,0.0,0.0,85.0], 'tau_decay':[50.0,20.0,20.0,20.0], 'tau_rise':[10.0,10.0,1.0,1.0]}) spike = nest.Create('spike_generator', params = {'spike_times': np.array([10.0])}) voltmeter = nest.Create('voltmeter', 1, {'withgid': True}) delays=[1.0, 300.0, 500.0, 700.0] w=[1.0, 1.0, 1.0, 1.0] for syn in range(4): nest.Connect(spike, neuron, syn_spec={'model': 'static_synapse', 'receptor_type': 1 + syn, 'weight': w[syn], 'delay': delays[syn]}) nest.Connect(voltmeter, neuron) nest.Simulate(1000.0) dmm = nest.GetStatus(voltmeter)[0] Vms = dmm["events"]["V_m"] ts = dmm["events"]["times"] import pylab pylab.figure(2) pylab.plot(ts, Vms) pylab.show()
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Author: Bruno Golosio 07/10/2016
SeeAlso: aeif_cond_alpha_multisynapse

class
aeif_cond_exp
: public Archiving_Node  #include <aeif_cond_exp.h>
Name: aeif_cond_exp  Conductance based exponential integrateandfire neuron model according to Brette and Gerstner (2005).
Description:
aeif_cond_exp is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with postsynaptic conductances in the form of truncated exponentials.
This implementation uses the embedded 4th order RungeKuttaFehlberg solver with adaptive stepsize to integrate the differential equation.
The membrane potential is given by the following differential equation:
\[\begin{split} C dV/dt= g_L(VE_L)+g_L*\Delta_T*\exp((VV_T)/\Delta_T)g_e(t)(VE_e) \\ g_i(t)(VE_i)w +I_e \end{split}\]and
\[ \tau_w * dw/dt= a(VE_L) W \]Note that the spike detection threshold V_peak is automatically set to \( V_th+10 mV \) to avoid numerical instabilites that may result from setting V_peak too high.
Parameters: The following parameters can be set in the status dictionary.
Dynamic state variables:
V_m
mV
Membrane potential
g_ex
nS
Excitatory synaptic conductance
g_in
nS
Inhibitory synaptic conductance
w
pA
Spikeadaptation current
Membrane Parameters
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_reset
mV
Reset value for V_m after a spike
E_L
mV
Leak reversal potential
g_L
nS
Leak conductance
I_e
pA
Constant external input current
Spike adaptation parameters
a
nS
Subthreshold adaptation
b
pA
Spiketriggered adaptation
Delta_T
mV
Slope factor
tau_w
ms
Adaptation time constant
V_th
mV
Spike initiation threshold
V_peak
mV
Spike detection threshold
Synaptic parameters
E_ex
mV
Excitatory reversal potential
tau_syn_ex
ms
Rise time of excitatory synaptic conductance (alpha function)
E_in
mV
Inhibitory reversal potential
tau_syn_in
ms
Rise time of the inhibitory synaptic conductance (alpha function)
Integration parameters
gsl_error_tol
real
This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.
Author: Adapted from aeif_cond_alpha by Lyle Muller; full revision by Tanguy Fardet on December 2016
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
 1
Brette R and Gerstner W (2005). Adaptive Exponential IntegrateandFire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:36373642. DOI: https://doi.org/10.1152/jn.00686.2005
SeeAlso: iaf_cond_exp, aeif_cond_alpha

class
aeif_psc_alpha
: public Archiving_Node  #include <aeif_psc_alpha.h>
Name: aeif_psc_alpha  Currentbased exponential integrateandfire neuron model according to Brette and Gerstner (2005).
Description:
aeif_psc_alpha is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005). Synaptic currents are modelled as alphafunctions.
This implementation uses the embedded 4th order RungeKuttaFehlberg solver with adaptive step size to integrate the differential equation.
The membrane potential is given by the following differential equation:
\[\begin{split} C dV/dt= g_L(VE_L)+g_L*\Delta_T*\exp((VV_T)/\Delta_T)g_e(t)(VE_e) \\ g_i(t)(VE_i)w +I_e \end{split}\]and
\[ \tau_w * dw/dt= a(VE_L) W \]Parameters:
The following parameters can be set in the status dictionary.
Dynamic state variables:
V_m
mV
Membrane potential
I_ex
pA
Excitatory synaptic current
dI_ex
pA/ms
First derivative of I_ex
I_in
pA
Inhibitory synaptic current
dI_in
pA/ms
First derivative of I_in
w
pA
Spikeadaptation current
g
pa
Spikeadaptation current
Membrane Parameters
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_reset
mV
Reset value for V_m after a spike
E_L
mV
Leak reversal potential
g_L
nS
Leak conductance
I_e
pA
Constant external input current
Spike adaptation parameters
a
ns
Subthreshold adaptation
b
pA
Spiketriggered adaptation
Delta_T
mV
Slope factor
tau_w
ms
Adaptation time constant
V_th
mV
Spike initiation threshold
V_peak
mV
Spike detection threshold
Synaptic parameters
tau_syn_ex
ms
Rise time of excitatory synaptic conductance (alpha function)
tau_syn_in
ms
Rise time of the inhibitory synaptic conductance (alpha function)
Integration parameters
gsl_error_tol
real
This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities
Author: Tanguy Fardet
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
References:
 1
Brette R and Gerstner W (2005). Adaptive Exponential IntegrateandFire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:36373642. DOI: https://doi.org/10.1152/jn.00686.2005
SeeAlso: iaf_psc_alpha, aeif_cond_exp

class
aeif_psc_delta
: public Archiving_Node  #include <aeif_psc_delta.h>
Name: aeif_psc_delta  Currentbased adaptive exponential integrateandfire neuron model according to Brette and Gerstner (2005) with delta synapse.
Description:
aeif_psc_delta is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with postsynaptic currents in the form of delta spikes.
This implementation uses the embedded 4th order RungeKuttaFehlberg solver with adaptive stepsize to integrate the differential equation.
The membrane potential is given by the following differential equation:
\[\begin{split} C dV/dt= g_L(VE_L)+g_L*\Delta_T*\exp((VV_T)/\Delta_T)g_e(t)(VE_e) \\ g_i(t)(VE_i)w +I_e \end{split}\]and
\[ \tau_w * dw/dt= a(VE_L) W \]\[ I(t) = J \sum_k \delta(t  t^k). \]Here delta is the dirac delta function and k indexes incoming spikes. This is implemented such that V_m will be incremented/decremented by the value of J after a spike.
Parameters:
The following parameters can be set in the status dictionary.
Dynamic state variables
V_m
mV
Membrane potential
w
pA
Spikeadaptation current
Membrane Parameters
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_reset
mV
Reset value for V_m after a spike
E_L
mV
Leak reversal potential
g_L
nS
Leak conductance
I_e
pA
Constant external input current
Spike adaptation parameters
a
ns
Subthreshold adaptation
b
pA
Spiketriggered adaptation
tau_w
ms
Adaptation time constant
Delta_T
mV
Slope factor
tau_w
ms
Adaptation time constant
V_th
mV
Spike initiation threshold
V_peak
mV
Spike detection threshold
Integration parameters
gsl_error_tol
real
This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.
Author: Mikkel Elle Lepperød adapted from aeif_psc_exp and iaf_psc_delta
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
References:
 1
Brette R and Gerstner W (2005). Adaptive Exponential IntegrateandFire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:36373642. DOI: https://doi.org/10.1152/jn.00686.2005
SeeAlso: iaf_psc_delta, aeif_cond_exp, aeif_psc_exp

class
aeif_psc_delta_clopath
: public Clopath_Archiving_Node  #include <aeif_psc_delta_clopath.h>
Name: aeif_psc_delta_clopath  Exponential integrateandfire neuron model according to Clopath et al. (2010).
Description:
aeif_psc_delta_clopath is an implementation of the neuron model as it is used in [1]. It is an extension of the aeif_psc_delta model and capable of connecting to a Clopath synapse.
Note that there are two points that are not mentioned in the paper but present in a MATLAB implementation by Claudia Clopath [3]. The first one is the clamping of the membrane potential to a fixed value after a spike occured to mimik a real spike and not just the upswing. This is important since the finite duration of the spike influences the evolution of the convolved versions (u_bar_[plus/minus]) of the membrane potential and thus the change of the synaptic weight. Secondly, there is a delay with which u_bar_[plus/minus] are used to compute the change of the synaptic weight.
Parameters:
The following parameters can be set in the status dictionary.
Dynamic state variables
V_m
mV
Membrane potential
w
pA
Spikeadaptation current
z
pA
Spikeadaptation current
V_th
mV
Adaptive spike initiation threshold
u_bar_plus
mV
Lowpass filtered Membrane potential
u_bar_minus
mV
Lowpass filtered Membrane potential
u_bar_bar
mV
Lowpass filtered u_bar_minus
Membrane Parameters
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_reset
mV
Reset value for V_m after a spike
E_L
mV
Leak reversal potential
g_L
nS
Leak conductance
I_e
pA
Constant external input current
tau_plus
ms
Time constant of u_bar_plus
tau_minus
ms
Time constant of u_bar_minus
tau_bar_bar
ms
Time constant of u_bar_bar
Spike adaptation parameters
a
nS
Subthreshold adaptation
b
pA
Spiketriggered adaptation
Delta_T
mV
Slope factor
tau_w
ms
Adaptation time constant
V_peak
mV
Spike detection threshold
V_th_max
mV
Value of V_th afer a spike
V_th_rest
mV
Resting value of V_th
Clopath rule parameters
A_LTD
1/mV
Amplitude of depression
A_LTP
1/mV^2
Amplitude of facilitation
theta_plus
mV
Threshold for u
theta_minus
mV
Threshold for u_bar_[plus/minus]
A_LTD_const
boolean
Flag that indicates whether A_LTD_ should be constant (true, default) or multiplied by u_bar_bar^2 / u_ref_squared (false).
delay_u_bars
real
Delay with which u_bar_[plus/minus] are processed to compute the synaptic weights.
U_ref_squared
real
Reference value for u_bar_bar_^2.
Other parameters
t_clamp
ms
Duration of clamping of Membrane potential after a spike
V_clamp
mV
Value to which the Membrane potential is clamped
Integration parameters
gsl_error_tol
real
This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.
Note:
Neither the clamping nor the delayed processing of u_bar_[plus/minus] are mentioned in [1]. However, they are part of an reference implementation by Claudia Clopath et al. that can be found on ModelDB [3]. The clamping is important to mimic a spike which is otherwise not described by the aeif neuron model.
Author: Jonas Stapmanns, David Dahmen, Jan Hahne
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
References:
 1
Clopath et al. (2010). Connectivity reflects coding: a model of voltagebased STDP with homeostasis. Nature Neuroscience 13(3):344352. DOI: https://doi.org/10.1038/nn.2479
 2
Clopath and Gerstner (2010). Voltage and spike timing interact in STDP – a unified model. Frontiers in Synaptic Neuroscience. 2:25 DOI: https://doi.org/10.3389/fnsyn.2010.00025
 3
Voltagebased STDP synapse (Clopath et al. 2010) on ModelDB https://senselab.med.yale.edu/ModelDB/showmodel.cshtml?model=144566&file=%2f modeldb_package%2fVoTriCode%2faEIF.m

class
aeif_psc_exp
: public Archiving_Node  #include <aeif_psc_exp.h>
Name: aeif_psc_exp  Currentbased exponential integrateandfire neuron model according to Brette and Gerstner (2005).
Description:
aeif_psc_exp is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with postsynaptic currents in the form of truncated exponentials.
This implementation uses the embedded 4th order RungeKuttaFehlberg solver with adaptive stepsize to integrate the differential equation.
The membrane potential is given by the following differential equation:
\[\begin{split} C dV/dt= g_L(VE_L)+g_L*\Delta_T*\exp((VV_T)/\Delta_T)g_e(t)(VE_e) \\ g_i(t)(VE_i)w +I_e \end{split}\]and
\[ \tau_w * dw/dt= a(VE_L) W \]Note that the spike detection threshold V_peak is automatically set to \( V_th+10 \) mV to avoid numerical instabilites that may result from setting V_peak too high.
Parameters:
The following parameters can be set in the status dictionary.
Dynamic state variables:
V_m
mV
Membrane potential
I_ex
pA
Excitatory synaptic current
I_in
pA
Inhibitory synaptic current
w
pA
Spikeadaptation current
Membrane Parameters
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_reset
mV
Reset value for V_m after a spike
E_L
mV
Leak reversal potential
g_L
nS
Leak conductance
I_e
pA
Constant external input current
Spike adaptation parameters
a
ns
Subthreshold adaptation
b
pA
Spiketriggered adaptation
Delta_T
mV
Slope factor
tau_w
ms
Adaptation time constant
V_t
mV
Spike initiation threshold
V_peak
mV
Spike detection threshold
Synaptic parameters
tau_syn_ex
ms
Rise time of excitatory synaptic conductance (alpha function)
tau_syn_in
ms
Rise time of the inhibitory synaptic conductance (alpha function)
Integration parameters
gsl_error_tol
real
This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities
Author: Tanguy Fardet
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
References:
 1
Brette R and Gerstner W (2005). Adaptive Exponential IntegrateandFire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:36373642. DOI: https://doi.org/10.1152/jn.00686.2005
SeeAlso: iaf_psc_exp, aeif_cond_exp

class
amat2_psc_exp
: public Archiving_Node  #include <amat2_psc_exp.h>
Name: amat2_psc_exp  Nonresetting leaky integrateandfire neuron model with exponential PSCs and adaptive threshold.
Description:
amat2_psc_exp is an implementation of a leaky integrateandfire model with exponential shaped postsynaptic currents (PSCs). Thus, postsynaptic currents have an infinitely short rise time.
The threshold is lifted when the neuron is fired and then decreases in a fixed time scale toward a fixed level [3].
The threshold crossing is followed by a total refractory period during which the neuron is not allowed to fire, even if the membrane potential exceeds the threshold. The membrane potential is NOT reset, but continuously integrated.
The linear subthresold dynamics is integrated by the Exact Integration scheme [1]. The neuron dynamics is solved on the time grid given by the computation step size. Incoming as well as emitted spikes are forced to that grid.
An additional state variable and the corresponding differential equation represents a piecewise constant external current.
The general framework for the consistent formulation of systems with neuron like dynamics interacting by point events is described in [1]. A flow chart can be found in [2].
Remarks:
The default parameter values for this model are different from the corresponding parameter values for mat2_psc_exp.
If identical parameters are used, and beta==0, then this model shall behave exactly as mat2_psc_exp.
The time constants in the model must fullfill the following conditions:
\( \tau_m != {\tau_{syn_{ex}}, \tau_{syn_{in}}} \)
\( \tau_v != {\tau_{syn_{ex}}, \tau_{syn_{in}}} \)
\( \tau_m != \tau_v \) This is required to avoid singularities in the numerics. This is a problem of implementation only, not a principal problem of the model.
Expect unstable numerics if time constants that are required to be different are very close.
Parameters:
The following parameters can be set in the status dictionary:
C_m
pF
Capacity of the membrane
E_L
mV
Resting potential
tau_m
ms
Membrane time constant
tau_syn_ex
ms
Time constant of postsynaptic excitatory currents
tau_syn_in
ms
Time constant of postsynaptic inhibitory currents
t_ref
ms
Duration of absolute refractory period (no spiking)
V_m
mV
Membrane potential
I_e
pA
Constant input current
t_spike
ms
Point in time of last spike
tau_1
ms
Short time constant of adaptive threshold [3, eqs 23]
tau_2
ms
Long time constant of adaptive threshold [3, eqs 23]
alpha_1
mV
Amplitude of short time threshold adaption [3, eqs 23]
alpha_2
mV
Amplitude of long time threshold adaption [3, eqs 23]
tau_v
ms
Time constant of kernel for voltagedependent threshold component [3, eqs 1617]
beta
1/ms
Scaling coefficient for voltagedependent threshold component [3, eqs 1617]
omega
mV
Resting spike threshold (absolute value, not relative to E_L as in [3])
State variables that can be read out with the multimeter device
V_m
mV
Nonresetting membrane potential
V_th
mV
Twotimescale adaptive threshold
Remarks:
\( \tau_m != \tau_{syn_{ex,in}} \) is required by the current implementation to avoid a degenerate case of the ODE describing the model [1]. For very similar values, numerics will be unstable.
References:
 1
Rotter S, Diesmann M (1999). Exact simulation of timeinvariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381402. DOI: https://doi.org/10.1007/s004220050570
 2
Diesmann M, Gewaltig MO, Rotter S, & Aertsen A (2001). State space analysis of synchronous spiking in cortical neural networks. Neurocomputing 3840:565571. DOI: https://doi.org/10.1016/S09252312(01)00409X
 3
Kobayashi R, Tsubo Y and Shinomoto S (2009). Madetoorder spiking neuron model equipped with a multitimescale adaptive threshold. Frontiers in Computational Neuroscience, 3:9. DOI: https://dx.doi.org/10.3389%2Fneuro.10.009.2009
 4
Yamauchi S, Kim H, Shinomoto S (2011). Elemental spiking neuron model for reproducing diverse firing patterns and predicting precise firing times. Frontiers in Computational Neuroscience, 5:42. DOI: https://doi.org/10.3389/fncom.2011.00042
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
FirstVersion: April 2013
Author: Thomas Heiberg & Hans E. Plesser (modified mat2_psc_exp model of Thomas Pfeil)

class
gainfunction_erfc
 #include <erfc_neuron.h>
Name: erfc_neuron  Binary stochastic neuron with complementary error function as activation function.
Description:
The erfc_neuron is an implementation of a binary neuron that is irregularly updated at Poisson time points. At each update point the total synaptic input h into the neuron is summed up, passed through a gain function g whose output is interpreted as the probability of the neuron to be in the active (1) state.
The gain function g used here is
\[ g(h) = 0.5 * erfc (( h  \theta ) / ( \sqrt( 2. ) * \sigma)). \]This corresponds to a McCullochPitts neuron receiving additional Gaussian noise with mean 0 and standard deviation sigma. The time constant tau_m is defined as the mean of the interupdateinterval that is drawn from an exponential distribution with this parameter. Using this neuron to reproduce simulations with asynchronous update (similar to [1,2]), the time constant needs to be chosen as tau_m = dt*N, where dt is the simulation time step and N the number of neurons in the original simulation with asynchronous update. This ensures that a neuron is updated on average every tau_m ms. Since in the original papers [1,2] neurons are coupled with zero delay, this implementation follows that definition. It uses the update scheme described in [3] to maintain causality: The incoming events in time step t_i are taken into account at the beginning of the time step to calculate the gain function and to decide upon a transition. In order to obtain delayed coupling with delay d, the user has to specify the delay d+h upon connection, where h is the simulation time step.
Remarks:
This neuron has a special use for spike events to convey the binary state of the neuron to the target. The neuron model only sends a spike if a transition of its state occurs. If the state makes an uptransition it sends a spike with multiplicity 2, if a down transition occurs, it sends a spike with multiplicity 1. The decoding scheme relies on the feature that spikes with multiplicity larger 1 are delivered consecutively, also in a parallel setting. The creation of double connections between binary neurons will destroy the decoding scheme, as this effectively duplicates every event. Using random connection routines it is therefore advisable to set the property ‘multapses’ to false. The neuron accepts several sources of currents, e.g. from a noise_generator.
Parameters:
tau_m
ms
Membrane time constant (mean interupdateinterval)
theta
mV
threshold for sigmoidal activation function
sigma
mV
1/sqrt(2pi) x inverse of maximal slope
References:
 1
Ginzburg I, Sompolinsky H (1994). Theory of correlations in stochastic neural networks. PRE 50(4) p. 3171 DOI: https://doi.org/10.1103/PhysRevE.50.3171
 2
McCulloch W, Pitts W (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5:115133. DOI: https://doi.org/10.1007/BF02478259
 3
Morrison A, Diesmann M (2007). Maintaining causality in discrete time neuronal simulations. In: Lectures in Supercomputational Neuroscience, p. 267. Peter beim Graben, Changsong Zhou, Marco Thiel, Juergen Kurths (Eds.), Springer. DOI: https://doi.org/10.1007/9783540731597_10
Sends: SpikeEvent
Receives: SpikeEvent, PotentialRequest
FirstVersion: May 2016
Authors: Jakob Jordan, Tobias Kuehn
SeeAlso: mcculloch_pitts_neuron, ginzburg_neuron

class
nonlinearities_gauss_rate
¶  #include <gauss_rate.h>
Name: gauss_rate  rate model with Gaussian gain function
Description:
gauss_rate is an implementation of a nonlinear rate model with input function
\[ input(h) = g * \exp( ( x  \mu )^2 / ( 2 * \sigma^2 ) ) \]. Input transformation can either be applied to individual inputs or to the sum of all inputs.The model supports connections to other rate models with either zero or nonzero delay, and uses the secondary_event concept introduced with the gapjunction framework.
Parameters:
The following parameters can be set in the status dictionary.
rate
real
Rate (unitless)
tau
ms
Time constant of rate dynamics
mu
real
Mean input
sigma
real
Noise parameter
g
real
Gain parameter
mu
real
Mean of the Gaussian gain function
sigma
real
Standard deviation of Gaussian gain function
linear_summation
boolean
Specifies type of nonlinearity (see above)
rectify_output
boolean
Switch to restrict rate to values >= 0
Note:
The boolean parameter linear_summation determines whether the input from different presynaptic neurons is first summed linearly and then transformed by a nonlinearity (true), or if the input from individual presynaptic neurons is first nonlinearly transformed and then summed up (false). Default is true.
References:
 1
Hahne J, Dahmen D, Schuecker J, Frommer A, Bolten M, Helias M, Diesmann M. (2017). Integration of continuoustime dynamics in a spiking neural network simulator. Frontiers in Neuroinformatics, 11:34. DOI: https://doi.org/10.3389/fninf.2017.00034
 2
Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann Mi (2015). A unified framework for spiking and gapjunction interactions in distributed neuronal network simulations. Frontiers in Neuroinformatics, 9:22. DOI: https://doi.org/10.3389/fninf.2015.00022
Sends: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent
Receives: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent, DataLoggingRequest
Author: Mario Senden, Jan Hahne, Jannis Schuecker
SeeAlso: rate_connection_instantaneous, rate_connection_delayed

class
gif_cond_exp
: public Archiving_Node  #include <gif_cond_exp.h>
Name: gif_cond_exp  Conductancebased generalized integrateandfire neuron model according to Mensi et al. (2012) and Pozzorini et al. (2015).
Description:
gif_psc_exp is the generalized integrateandfire neuron according to Mensi et al. (2012) and Pozzorini et al. (2015), with postsynaptic conductances in the form of truncated exponentials.
This model features both an adaptation current and a dynamic threshold for spikefrequency adaptation. The membrane potential (V) is described by the differential equation:
\[ C*dV(t)/dt = g_L*(V(t)E_L)  \eta_1(t)  \eta_2(t)  \ldots  \eta_n(t) + I(t) \]where each \( \eta_i \) is a spiketriggered current (stc), and the neuron model can have arbitrary number of them. Dynamic of each \( \eta_i \) is described by:
\[ \tau_\eta{_i}*d{\eta_i}/dt = \eta_i \]and in case of spike emission, its value increased by a constant (which can be positive or negative):
\[ \eta_i = \eta_i + q_{\eta_i} \text{ (in case of spike emission).} \]Neuron produces spikes STOCHASTICALLY according to a point process with the firing intensity:
\[ \lambda(t) = \lambda_0 * \exp (V(t)V_T(t)) / \Delta_V \]where \( V_T(t) \) is a timedependent firing threshold:
\[ V_T(t) = V_{T_star} + \gamma_1(t) + \gamma_2(t) + \ldots + \gamma_m(t) \]where \( \gamma_i \) is a kernel of spikefrequency adaptation (sfa), and the neuron model can have arbitrary number of them. Dynamic of each \( \gamma_i \) is described by:
\[ \tau_{\gamma_i}*d\gamma_i/dt = \gamma_i \]and in case of spike emission, its value increased by a constant (which can be positive or negative):\[ \gamma_i = \gamma_i + q_{\gamma_i} \text{ (in case of spike emission).} \]Note:
In the current implementation of the model (as described in [1] and [2]), the values of \( \eta_i \) and \( \gamma_i \) are affected immediately after spike emission. However, GIF toolbox (http://wiki.epfl.ch/giftoolbox) which fits the model using experimental data, requires a different set of \( \eta_i \) and \( \gamma_i\) . It applies the jump of \( \eta_i \) and \( \gamma_i \) after the refractory period. One can easily convert between \( q_\eta/\gamma \) of these two approaches: \( q{_\eta}_{giftoolbox} = q_{\eta_{NEST}} * (1  \exp( \tau_{ref} / \tau_\eta )) \) The same formula applies for \( q_{\gamma} \).
The shape of synaptic conductance is exponential.
Parameters:
The following parameters can be set in the status dictionary.
Membrane Parameters
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_reset
mV
Reset value for V_m after a spike
E_L
mV
Leak reversal potential
g_L
nS
Leak conductance
I_e
pA
Constant external input current
Spike adaptation and firing intensity parameters
q_stc
list of nA
Values added to spiketriggered currents (stc) after each spike emission
tau_stc
list of ms
Time constants of stc variables
q_sfa
list of mV
Values added to spikefrequency adaptation (sfa) after each spike emission
tau_sfa
list of ms
Time constants of sfa variables
Delta_V
mV
Stochasticity level
lambda_0
real
Stochastic intensity at firing threshold V_T i n 1/s.
V_T_star
mV
Base threshold
Synaptic parameters
E_ex
mV
Excitatory reversal potential
tau_syn_ex
ms
Decay time of excitatory synaptic conductance
E_in
mV
Inhibitory reversal potential
tau_syn_in
ms
Decay time of the inhibitory synaptic conductance
Integration parameters
gsl_error_tol
real
This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.
References:
 1
Mensi S, Naud R, Pozzorini C, Avermann M, Petersen CC, Gerstner W (2012) Parameter extraction and classification of three cortical neuron types reveals two distinct adaptation mechanisms. Journal of Neurophysiology, 107(6):17561775. DOI: https://doi.org/10.1152/jn.00408.2011
 2
Pozzorini C, Mensi S, Hagens O, Naud R, Koch C, Gerstner W (2015). Automated highthroughput characterization of single neurons by means of simplified spiking models. PLoS Computational Biology, 11(6), e1004275. DOI: https://doi.org/10.1371/journal.pcbi.1004275
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Author: March 2016, Setareh
SeeAlso: pp_psc_delta, gif_cond_exp_multisynapse, gif_psc_exp, gif_psc_exp_multisynapse

class
gainfunction_ginzburg
 #include <ginzburg_neuron.h>
Name: ginzburg_neuron  Binary stochastic neuron with sigmoidal activation function.
Description:
The ginzburg_neuron is an implementation of a binary neuron that is irregularly updated as Poisson time points. At each update point the total synaptic input h into the neuron is summed up, passed through a gain function g whose output is interpreted as the probability of the neuron to be in the active (1) state.
The gain function g used here is \( g(h) = c1*h + c2 * 0.5*(1 + \tanh(c3*(h\theta))) \) (output clipped to [0,1]). This allows to obtain affinlinear (c1!=0, c2!=0, c3=0) or sigmoidal (c1=0, c2=1, c3!=0) shaped gain functions. The latter choice corresponds to the definition in [1], giving the name to this neuron model. The choice c1=0, c2=1, c3=beta/2 corresponds to the Glauber dynamics [2], \( g(h) = 1 / (1 + \exp(\beta (h\theta))) \). The time constant \( \tau_m \) is defined as the mean interupdateinterval that is drawn from an exponential distribution with this parameter. Using this neuron to reprodce simulations with asynchronous update [1], the time constant needs to be chosen as \( \tau_m = dt*N \), where dt is the simulation time step and N the number of neurons in the original simulation with asynchronous update. This ensures that a neuron is updated on average every \( \tau_m \) ms. Since in the original paper [1] neurons are coupled with zero delay, this implementation follows this definition. It uses the update scheme described in [3] to maintain causality: The incoming events in time step \( t_i \) are taken into account at the beginning of the time step to calculate the gain function and to decide upon a transition. In order to obtain delayed coupling with delay d, the user has to specify the delay d+h upon connection, where h is the simulation time step.
Remarks:
This neuron has a special use for spike events to convey the binary state of the neuron to the target. The neuron model only sends a spike if a transition of its state occurs. If the state makes an uptransition it sends a spike with multiplicity 2, if a down transition occurs, it sends a spike with multiplicity 1. The decoding scheme relies on the feature that spikes with multiplicity larger 1 are delivered consecutively, also in a parallel setting. The creation of double connections between binary neurons will destroy the deconding scheme, as this effectively duplicates every event. Using random connection routines it is therefore advisable to set the property ‘multapses’ to false. The neuron accepts several sources of currents, e.g. from a noise_generator.
Parameters:
tau_m
ms
Membrane time constant (mean interupdateinterval)
theta
mV
Threshold for sigmoidal activation function
c1
probability/ mV
Linear gain factor
c2
probability
Prefactor of sigmoidal gain
c3
1/mV
Slope factor of sigmoidal gain
References:
 1
Ginzburg I, Sompolinsky H (1994). Theory of correlations in stochastic neural networks. PRE 50(4) p. 3171 DOI: https://doi.org/10.1103/PhysRevE.50.3171
 2
Hertz J, Krogh A, Palmer R (1991). Introduction to the theory of neural computation. AddisonWesley Publishing Conmpany.
 3
Morrison A, Diesmann M (2007). Maintaining causality in discrete time neuronal simulations. In: Lectures in Supercomputational Neuroscience, p. 267. Peter beim Graben, Changsong Zhou, Marco Thiel, Juergen Kurths (Eds.), Springer. DOI: https://doi.org/10.1007/9783540731597_10
Sends: SpikeEvent
Receives: SpikeEvent, PotentialRequest
FirstVersion: February 2010
Author: Moritz Helias
SeeAlso: pp_psc_delta

class
hh_cond_beta_gap_traub
: public Archiving_Node  #include <hh_cond_beta_gap_traub.h>
Name: hh_cond_beta_gap_traub  modified HodgkinHuxley neuron as featured in Brette et al (2007) review with added gap junction support and beta function synaptic conductance.
Description:
hh_cond_beta_gap_traub is an implementation of a modified HodgkinHuxley model that also supports gap junctions.
This model was specifically developed for a major review of simulators [1], based on a model of hippocampal pyramidal cells by Traub and Miles[2]. The key differences between the current model and the model in [2] are:
This model is a point neuron, not a compartmental model.
This model includes only I_Na and I_K, with simpler I_K dynamics than in [2], so it has only three instead of eight gating variables; in particular, all Ca dynamics have been removed.
Incoming spikes induce an instantaneous conductance change followed by exponential decay instead of activation over time.
This model is primarily provided as reference implementation for hh_coba example of the Brette et al (2007) review. Default parameter values are chosen to match those used with NEST 1.9.10 when preparing data for [1]. Code for all simulators covered is available from ModelDB [3].
Note: In this model, a spike is emitted if
\[ V_m >= V_T + 30 mV and V_m has fallen during the current time step \]To avoid that this leads to multiple spikes during the falling flank of a spike, it is essential to chose a sufficiently long refractory period. Traub and Miles used \( t_ref = 3 ms \) [2, p 118], while we used \( t_ref = 2 ms \) in [2].
Postsynaptic currents Incoming spike events induce a postsynaptic change of conductance modelled by a beta function as outlined in [4,5]. The beta function is normalised such that an event of weight 1.0 results in a peak current of 1 nS at \( t = tau_rise_xx \) where xx is ex or in.
Spike Detection Spike detection is done by a combined thresholdandlocalmaximum search: if there is a local maximum above a certain threshold of the membrane potential, it is considered a spike.
Gap Junctions Gap Junctions are implemented by a gap current of the form \( g_ij( V_i  V_j) \).
Parameters:
The following parameters can be set in the status dictionary.
V_m
mV
Membrane potential
V_T
mV
Voltage offset that controls dynamics. For default parameters, V_T = 63mV results in a threshold around 50mV
E_L
mV
Leak reversal potential
C_m
pF
Capacity of the membrane
g_L
nS
Leak conductance
tau_rise_ex
ms
Excitatory synaptic beta function rise time
tau_decay_ex
ms
Excitatory synaptic beta function decay time
tau_rise_in
ms
Inhibitory synaptic beta function rise time
tau_decay_in
ms
Inhibitory synaptic beta function decay time
t_ref
ms
Duration of refractory period (see Note)
E_ex
mV
Excitatory synaptic reversal potential
E_in
mV
Inhibitory synaptic reversal potential
E_Na
mV
Sodium reversal potential
g_Na
nS
Sodium peak conductance
E_K
mV
Potassium reversal potential
g_K
nS
Potassium peak conductance
I_e
pA
External input current
References:
 1
Brette R et al (2007). Simulation of networks of spiking neurons: A review of tools and strategies. Journal of Computational Neuroscience 23:34998. DOI: https://doi.org/10.1007/s1082700700386
 2
Traub RD and Miles R (1991). Neuronal Networks of the Hippocampus. Cambridge University Press, Cambridge UK.
 3
 4
Rotter S and Diesmann M (1999). Exact digital simulation of timeinvariant linear systems with applications to neuronal modeling. Biological Cybernetics 81:381 DOI: https://doi.org/10.1007/s004220050570
 5
Roth A and van Rossum M (2010). Chapter 6: Modeling synapses. in De Schutter, Computational Modeling Methods for Neuroscientists, MIT Press.
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Author: Daniel Naoumenko (modified hh_cond_exp_traub by Schrader and hh_psc_alpha_gap by Jan Hahne, Moritz Helias and Susanne Kunkel)
SeeAlso: hh_psc_alpha_gap, hh_cond_exp_traub, gap_junction, iaf_cond_beta

class
hh_psc_alpha
: public Archiving_Node  #include <hh_psc_alpha.h>
Name: hh_psc_alpha  HodgkinHuxley neuron model.
Description:
hh_psc_alpha is an implementation of a spiking neuron using the HodgkinHuxley formalism.
Postsynaptic currents Incoming spike events induce a postsynaptic change of current modelled by an alpha function. The alpha function is normalised such that an event of weight 1.0 results in a peak current of 1 pA.
Spike Detection Spike detection is done by a combined thresholdandlocalmaximum search: if there is a local maximum above a certain threshold of the membrane potential, it is considered a spike.
Parameters:
The following parameters can be set in the status dictionary.
V_m
mV
Membrane potential
E_L
mV
Leak reversal potential
C_m
pF
Capacity of the membrane
g_L
nS
Leak conductance
tau_ex
ms
Rise time of the excitatory synaptic alpha function
tau_in
ms
Rise time of the inhibitory synaptic alpha function
E_Na
mV
Sodium reversal potential
g_Na
nS
Sodium peak conductance
E_K
mV
Potassium reversal potential
g_K
nS
Potassium peak conductance
Act_m
real
Activation variable m
Act_h
real
Activation variable h
Inact_n
real
Inactivation variable n
I_e
pA
External input current
Problems/Todo:
better spike detection initial wavelet/spike at simulation onset
References:
 1
Gerstner W, Kistler W (2002). Spiking neuron models: Single neurons, populations, plasticity. New York: Cambridge University Press
 2
Dayan P, Abbott LF (2001). Theoretical neuroscience: Computational and mathematical modeling of neural systems. Cambridge, MA: MIT Press. https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_3006127>
 3
Hodgkin AL and Huxley A F (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 117. DOI: https://doi.org/10.1113/jphysiol.1952.sp004764
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Authors: Schrader
SeeAlso: hh_cond_exp_traub

class
hh_psc_alpha_clopath
: public Clopath_Archiving_Node  #include <hh_psc_alpha_clopath.h>
Name: hh_psc_alpha_clopath  HodgkinHuxley neuron model with support for the Clopath synapse.
Description:
hh_psc_alpha_clopath is an implementation of a spiking neuron using the HodgkinHuxley formalism and that is capable of connecting to a Clopath synapse.
(1) Postsynaptic currents Incoming spike events induce a postsynaptic change of current modelled by an alpha function. The alpha function is normalised such that an event of weight 1.0 results in a peak current of 1 pA.
(2) Spike Detection Spike detection is done by a combined thresholdandlocalmaximum search: if there is a local maximum above a certain threshold of the membrane potential, it is considered a spike.
Parameters:
The following parameters can be set in the status dictionary.
Dynamic state variables
V_m
mV
Membrane potential
u_bar_plus
mV
Lowpass filtered Membrane potential
u_bar_minus
mV
Lowpass filtered Membrane potential
u_bar_bar
mV
Lowpass filtered u_bar_minus
Membrane Parameters
E_L
mV
Leak reversal potential
C_m
pF
Capacity of the membrane
g_L
nS
Leak conductance
tau_ex
ms
Rise time of the excitatory synaptic alpha function
tau_in
ms
Rise time of the inhibitory synaptic alpha function
E_Na
mV
Sodium reversal potential
g_Na
nS
Sodium peak conductance
E_K
mV
Potassium reversal potential
g_K
nS
Potassium peak conductance
Act_m
real
Activation variable m
Act_h
real
Activation variable h
Inact_n
real
Inactivation variable n
I_e
pA
External input current
Clopath rule parameters
A_LTD
1/mV
Amplitude of depression
A_LTP
1/mV^2
Amplitude of facilitation
theta_plus
mV
Threshold for u
theta_minus
mV
Threshold for u_bar_[plus/minus]
A_LTD_const
boolean
Flag that indicates whether A_LTD_ should be constant (true, default) or multiplied by u_bar_bar^2 / u_ref_squared (false).
delay_u_bars
real
Delay with which u_bar_[plus/minus] are processed to compute the synaptic weights.
U_ref_squared
real
Reference value for u_bar_bar_^2.
Problems/Todo:
better spike detection initial wavelet/spike at simulation onset
References:
 1
Gerstner W and Kistler WM (2002). Spiking neuron models: Single neurons, populations, plasticity. New York: Cambridge university press.
 2
Dayan P and Abbott L (2001). Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. Cambridge, MA: MIT Press. https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_3006127
 3
Hodgkin AL and Huxley A F (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 117. DOI: https://doi.org/10.1113/jphysiol.1952.sp004764
 4
Clopath et al. (2010). Connectivity reflects coding: a model of voltagebased STDP with homeostasis. Nature Neuroscience 13(3):344352. DOI: https://doi.org/10.1038/nn.2479
 5
Clopath and Gerstner (2010). Voltage and spike timing interact in STDP – a unified model. Frontiers in Synaptic Neuroscience. 2:25 DOI: https://doi.org/10.3389/fnsyn.2010.00025
 6
Voltagebased STDP synapse (Clopath et al. 2010) connected to a HodgkinHuxley neuron on ModelDB: https://senselab.med.yale.edu/ModelDB/showmodel.cshtml?model=144566&file =%2fmodeldb_package%2fstdp_cc.mod
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Author: Jonas Stapmanns, David Dahmen, Jan Hahne (adapted from hh_psc_alpha by Schrader)
SeeAlso: hh_psc_alpha, clopath_synapse, aeif_psc_delta_clopath

class
hh_psc_alpha_gap
: public Archiving_Node  #include <hh_psc_alpha_gap.h>
Name: hh_psc_alpha_gap  HodgkinHuxley neuron model with gapjunction support.
Description:
hh_psc_alpha_gap is an implementation of a spiking neuron using the HodgkinHuxley formalism. In contrast to hh_psc_alpha the implementation additionally supports gap junctions.
Postsynaptic currents Incoming spike events induce a postsynaptic change of current modelled by an alpha function. The alpha function is normalised such that an event of weight 1.0 results in a peak current of 1 pA.
Spike Detection Spike detection is done by a combined thresholdandlocalmaximum search: if there is a local maximum above a certain threshold of the membrane potential, it is considered a spike.
Gap Junctions Gap Junctions are implemented by a gap current of the form \( g_ij( V_i  V_j) \).
Parameters:
The following parameters can be set in the status dictionary.
tau_ex
ms
Rise time of the excitatory synaptic alpha function
tau_in
ms
Rise time of the inhibitory synaptic alpha function
g_K
nS
Potassium peak conductance
V_m
mV
Membrane potential
E_L
mV
Leak reversal potential
g_L
nS
Leak conductance
C_m
pF
Capacity of the membrane
tau_syn_ex
ms
Rise time of the excitatory synaptic alpha function
tau_syn_in
ms
Rise time of the inhibitory synaptic alpha function
E_Na
mV
Sodium reversal potential
g_Na
nS
Sodium peak conductance
E_K
mV
Potassium reversal potential
g_Kv1
nS
Potassium peak conductance
g_Kv3
nS
Potassium peak conductance
Act_m
real
Activation variable m
Act_h
real
Activation variable h
Inact_n
real
Inactivation variable n
I_e
pA
External input current
References:
 1
Gerstner W, Kistler W. Spiking neuron models: Single neurons, populations, plasticity. Cambridge University Press
 2
Mancilla JG, Lewis TG, Pinto DJ, Rinzel J, Connors BW (2007). Synchronization of electrically coupled pairs of inhibitory interneurons in neocortex, Journal of Neurosciece, 27:20582073 DOI: https://doi.org/10.1523/JNEUROSCI.271506.2007 (parameters taken from here)
 3
Hodgkin AL and Huxley A F (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 117. DOI: https://doi.org/10.1113/jphysiol.1952.sp004764
 4
Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M (2015). A unified framework for spiking and gapjunction interactions in distributed neuronal netowrk simulations. Frontiers in Neuroinformatics, 9:22. DOI: https://doi.org/10.3389/fninf.2015.00022
Sends: SpikeEvent, GapJunctionEvent
Receives: SpikeEvent, GapJunctionEvent, CurrentEvent, DataLoggingRequest
Author: Jan Hahne, Moritz Helias, Susanne Kunkel
SeeAlso: hh_psc_alpha, hh_cond_exp_traub, gap_junction

class
ht_neuron
: public Archiving_Node  #include <ht_neuron.h>
Name: ht_neuron  Neuron model after Hill & Tononi (2005).
Description:
This model neuron implements a slightly modified version of the neuron model described in [1]. The most important properties are:
Integrateandfire with threshold adaptive threshold.
Repolarizing potassium current instead of hard reset.
AMPA, NMDA, GABA_A, and GABA_B conductancebased synapses with betafunction (difference of exponentials) time course.
Voltagedependent NMDA with instantaneous or twostage unblocking [1, 2].
Intrinsic currents I_h, I_T, I_Na(p), and I_KNa.
Synaptic “minis” are not implemented.
Documentation and Examples:
docs/model_details/HillTononiModels.ipynb
pynest/examples/intrinsic_currents_spiking.py
pynest/examples/intrinsic_currents_subthreshold.py
Parameters:
V_m
mV
Membrane potential
tau_m
ms
Membrane time constant applying to all currents except repolarizing Kcurrent (see [1], p 1677)
t_ref
ms
Refractory time and duration of postspike repolarizing potassium current (t_spike in [1])
tau_spike
ms
Membrane time constant for postspike repolarizing potassium current
voltage_clamp
boolean
If true, clamp voltage to value at beginning of simulation (default: false, mainly for testing)
theta
mV
Threshold
theta_eq
mV
Equilibrium value
tau_theta
ms
Time constant
g_KL
nS
Conductance for potassium leak current
E_K
mV
Reversal potential for potassium leak currents
g_NaL
nS
Conductance for sodium leak currents
E_Na
mV
Reversal potential for Na leak currents
tau_D_KNa
ms
Relaxation time constant for I_KNa
receptor_types
Dictionary mapping synapse names to ports on neuron model
recordables
List of recordable quantities
{E_rev,g_peak,tau_rise,tau_decay}_{AMPA,NMDA,GABA_A,GABA_B}
Reversal potentials, peak conductances and time constants for synapses (tau_rise/tau_decay correspond to tau_1/tau_2 in the paper)
V_act_NMDA, S_act_NMDA, tau_Mg_{fast, slow}_NMDA
Parameters for voltage dependence of NMDA conductance, see above
nstant_unblock_NMDA
Instantaneous NMDA unblocking (default: false)
{E_rev,g_peak}_{h,T,NaP,KNa}
Reversal potential and peak conductance for intrinsic currents
equilibrate
If given and true, timedependent activation and inactivation state variables (h, m) of intrinsic currents and NMDA channels are set to their equilibrium values during this SetStatus call; otherwise they retain their present values.
Conductances are unitless in this model and currents are in mV.
Author: Hans Ekkehard Plesser
Sends: SpikeEvent Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
FirstVersion: October 2009; full revision November 2016
References:
 1
Hill S, Tononi G (2005). Modeling sleep and wakefulness in the thalamocortical system. Journal of Neurophysiology. 93:16711698. DOI: https://doi.org/10.1152/jn.00915.2004
 2
VargasCaballero M, Robinson HPC (2003). A slow fraction of Mg2+ unblock of NMDA receptors limits their contribution to spike generation in cortical pyramidal neurons. Journal of Neurophysiology 89:27782783. DOI: https://doi.org/10.1152/jn.01038.2002
SeeAlso: ht_connection

class
iaf_chs_2007
: public Archiving_Node  #include <iaf_chs_2007.h>
Name: iaf_chs_2007  Spikeresponse model used in Carandini et al 2007.
Description:
The membrane potential is the sum of stereotyped events: the postsynaptic potentials (V_syn), waveforms that include a spike and the subsequent afterhyperpolarization (V_spike) and Gaussiandistributed white noise.
The postsynaptic potential is described by alpha function where U_epsp is the maximal amplitude of the EPSP and tau_epsp is the time to peak of the EPSP.
The spike waveform is described as a delta peak followed by a membrane potential reset and exponential decay. U_reset is the magnitude of the reset/afterhyperpolarization and tau_reset is the time constant of recovery from this hyperpolarization.
The linear subthresold dynamics is integrated by the Exact Integration scheme [1]. The neuron dynamics is solved on the time grid given by the computation step size. Incoming as well as emitted spikes are forced to that grid.
Remarks: The way the noise term was implemented in the original model makes it unsuitable for simulation in NEST. The workaround was to prepare the noise signal externally prior to simulation. The noise signal, if present, has to be at least as long as the simulation.
Parameters:
The following parameters can be set in the status dictionary.
tau_epsp
ms
Membrane time constant
tau_reset
ms
Refractory time constant
U_epsp
real
Maximum amplitude of the EPSP, normalized
U_reset
real
Reset value of the membrane potential, normalized
U_noise
real
Noise scale, normalized
noise
list of real
Noise signal
References:
 1
Carandini M, Horton JC, Sincich LC (2007). Thalamic filtering of retinal spike trains by postsynaptic summation. Journal of Vision 7(14):20,111. DOI: https://doi.org/10.1167/7.14.20
 2
Rotter S, Diesmann M (1999). Exact simulation of timeinvariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381402. DOI: https://doi.org/10.1007/s004220050570
Sends: SpikeEvent
Receives: SpikeEvent, DataLoggingRequest
FirstVersion: May 2012
Author: Thomas Heiberg, Birgit Kriener

class
iaf_chxk_2008
: public Archiving_Node  #include <iaf_chxk_2008.h>
Name: iaf_chxk_2008  Conductance based leaky integrateandfire neuron model used in Casti et al 2008.
Description:
iaf_chxk_2008 is an implementation of a spiking neuron using IAF dynamics with conductancebased synapses [1]. It is modeled after iaf_cond_alpha with the addition of after hyperpolarization current instead of a membrane potential reset. Incoming spike events induce a postsynaptic change of conductance modeled by an alpha function. The alpha function is normalized such that an event of weight 1.0 results in a peak current of 1 nS at \( t = tau_{syn} \).
Parameters:
The following parameters can be set in the status dictionary.
V_m
mV
Membrane potential
E_L
mV
Leak reversal potential
C_m
pF
Capacity of the membrane
V_th
mV
Spike threshold
E_ex
mV
Excitatory reversal potential
E_in
mV
Inhibitory reversal potential
g_L
nS
Leak conductance
tau_ex
ms
Rise time of the excitatory synaptic alpha function
tau_in
ms
Rise time of the inhibitory synaptic alpha function
I_e
pA
Constant input current
tau_ahp
ms
Afterhyperpolarization (AHP) time constant
E_ahp
mV
AHP potential
g_ahp
nS
AHP conductance
ahp_bug
boolean
Defaults to false. If true, behaves like original model implementation
References:
 1
Casti A, Hayot F, Xiao Y, Kaplan E (2008) A simple model of retinaLGN transmission. Journal of Computational Neuroscience 24:235252. DOI: https://doi.org/10.1007/s1082700700537
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent
Author: Heiberg
SeeAlso: iaf_cond_alpha

class
iaf_cond_alpha
: public Archiving_Node  #include <iaf_cond_alpha.h>
Name: iaf_cond_alpha  Simple conductance based leaky integrateandfire neuron model.
Description:
iaf_cond_alpha is an implementation of a spiking neuron using IAF dynamics with conductancebased synapses. Incoming spike events induce a postsynaptic change of conductance modelled by an alpha function. The alpha function is normalised such that an event of weight 1.0 results in a peak current of 1 nS at \( t = tau_{syn} \).
Parameters:
The following parameters can be set in the status dictionary.
V_m
mV
Membrane potential
E_L
mV
Leak reversal potential
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_th
mV
Spike threshold
V_reset
mV
Reset potential of the membrane
E_ex
mV
Excitatory reversal potential
E_in
mV
Inhibitory reversal potential
g_L
nS
Leak conductance
tau_syn_ex
ms
Rise time of the excitatory synaptic alpha function
tau_syn_in
ms
Rise time of the inhibitory synaptic alpha function
I_e
pA
Constant input current
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Remarks:
References:
 Note
Per 20090417, this class has been revised to our newest insights into class design. Please use THIS CLASS as a reference when designing your own models with nonlinear dynamics. One weakness of this class is that it distinguishes between inputs to the two synapses by the sign of the synaptic weight. It would be better to use receptor_types, cf iaf_cond_alpha_mc.
 1
Meffin H, Burkitt AN, Grayden DB (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. Journal of Computational Neuroscience, 16:159175. DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81
 2
Bernander O, Douglas RJ, Martin KAC, Koch C (1991). Synaptic background activity influences spatiotemporal integration in single pyramidal cells. Proceedings of the National Academy of Science USA, 88(24):1156911573. DOI: https://doi.org/10.1073/pnas.88.24.11569
 3
Kuhn A, Rotter S (2004) Neuronal integration of synaptic input in the fluctuation driven regime. Journal of Neuroscience, 24(10):23452356 DOI: https://doi.org/10.1523/JNEUROSCI.334903.2004
Author: Schrader, Plesser
SeeAlso: iaf_cond_exp, iaf_cond_alpha_mc

class
iaf_cond_alpha_mc
: public Archiving_Node  #include <iaf_cond_alpha_mc.h>
Name: iaf_cond_alpha_mc  PROTOTYPE Multicompartment conductancebased leaky integrateandfire neuron model.
Description:
THIS MODEL IS A PROTOTYPE FOR ILLUSTRATION PURPOSES. IT IS NOT YET FULLY TESTED. USE AT YOUR OWN PERIL!
iaf_cond_alpha_mc is an implementation of a multicompartment spiking neuron using IAF dynamics with conductancebased synapses. It serves mainly to illustrate the implementation of multicompartment models in NEST.
The model has three compartments: soma, proximal and distal dendrite, labeled as s, p, and d, respectively. Compartments are connected through passive conductances as follows
\[\begin{split} C_{m.s} d/dt V_{m.s} = \ldots  g_{sp} ( V_{m.s}  V_{m.p} ) \\ C_{m.p} d/dt V_{m.p} = \ldots  g_{sp} ( V_{m.p}  V_{m.s} )  g_{pd} ( V_{m.p}  V_{m.d} ) \\ C_{m.d} d/dt V_{m.d} = \ldots \qquad  g_{pd} ( V_{m.d}  V_{m.p} ) \end{split}\]A spike is fired when the somatic membrane potential exceeds threshold, \( V_{m.s} >= V_{th} \). After a spike, somatic membrane potential is clamped to a reset potential, \( V_{m.s} == V_{reset} \), for the refractory period. Dendritic membrane potentials are not manipulated after a spike.There is one excitatory and one inhibitory conductancebased synapse onto each compartment, with alphafunction time course. The alpha function is normalised such that an event of weight 1.0 results in a peak current of 1 nS at t = tau_syn. Each compartment can also receive current input from a current generator, and an external (rheobase) current can be set for each compartment.
Synapses, including those for injection external currents, are addressed through the receptor types given in the receptor_types entry of the state dictionary. Note that in contrast to the singlecompartment iaf_cond_alpha model, all synaptic weights must be positive numbers!
Parameters:
The following parameters can be set in the status dictionary. Parameters for each compartment are collected in a subdictionary; these subdictionaries are called “soma”, “proximal”, and “distal”, respectively. In the list below, these parameters are marked with an asterisk.
V_m*
mV
Membrane potential
E_L*
mV
Leak reversal potential
C_m*
pF
Capacity of the membrane
E_ex*
mV
Excitatory reversal potential
E_in*
mV
Inhibitory reversal potential
g_L*
nS
Leak conductance
tau_syn_ex*
ms
Rise time of the excitatory synaptic alpha function
tau_syn_in*
ms
Rise time of the inhibitory synaptic alpha function
I_e*
pA
Constant input current
g_sp
nS
Conductance connecting soma and proximal dendrite
g_pd
nS
Conductance connecting proximal and distal dendrite
t_ref
ms
Duration of refractory period
V_th
mV
Spike threshold in mV
V_reset
mV
Reset potential of the membrane
Example: See pynest/examples/mc_neuron.py.
Remarks:
This is a prototype for illustration which has undergone only limited testing. Details of the implementation and userinterface will likely change. USE AT YOUR OWN PERIL!
Sends: SpikeEvent
 Note
All parameters that occur for both compartments and dendrite are stored as C arrays, with index 0 being soma.
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
References:
 1
Meffin H, Burkitt AN, Grayden DB (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. Journal of Computational Neuroscience, 16:159175. DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81
 2
Bernander O, Douglas RJ, Martin KAC, Koch C (1991). Synaptic background activity influences spatiotemporal integration in single pyramidal cells. Proceedings of the National Academy of Science USA, 88(24):1156911573. DOI: https://doi.org/10.1073/pnas.88.24.11569
Author: Plesser
SeeAlso: iaf_cond_alpha

class
iaf_cond_beta
: public Archiving_Node  #include <iaf_cond_beta.h>
Name: iaf_cond_beta  Simple conductance based leaky integrateandfire neuron model.
Description:
iaf_cond_beta is an implementation of a spiking neuron using IAF dynamics with conductancebased synapses. Incoming spike events induce a postsynaptic change of conductance modelled by an beta function. The beta function is normalised such that an event of weight 1.0 results in a peak current of 1 nS at t = tau_rise_[exin].
Parameters:
The following parameters can be set in the status dictionary.
V_m
mV
Membrane potential
E_L
mV
Leak reversal potential
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_th
mV
Spike threshold
V_reset
mV
Reset potential of the membrane
E_ex
mV
Excitatory reversal potential
E_in
mV
Inhibitory reversal potential
g_L
nS
Leak conductance
tau_syn_ex
ms
Rise time of the excitatory synaptic alpha function
tau_decay_ex
ms
Rise time of the excitatory synaptic beta function
tau_syn_in
ms
Rise time of the inhibitory synaptic alpha function
tau_decay_in
ms
Rise time of the inhibitory synaptic beta function
I_e
pA
Constant input current
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Remarks:
References:
 Note
Per 20090417, this class has been revised to our newest insights into class design. Please use THIS CLASS as a reference when designing your own models with nonlinear dynamics. One weakness of this class is that it distinguishes between inputs to the two synapses by the sign of the synaptic weight. It would be better to use receptor_types, cf iaf_cond_alpha_mc.
 1
Meffin H, Burkitt AN, Grayden DB (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. Journal of Computational Neuroscience, 16:159175. DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81
 2
Bernander O, Douglas RJ, Martin KAC, Koch C (1991). Synaptic background activity influences spatiotemporal integration in single pyramidal cells. Proceedings of the National Academy of Science USA, 88(24):1156911573. DOI: https://doi.org/10.1073/pnas.88.24.11569
 3
Kuhn A, Rotter S (2004) Neuronal integration of synaptic input in the fluctuation driven regime. Journal of Neuroscience, 24(10):23452356 DOI: https://doi.org/10.1523/JNEUROSCI.334903.2004
 4
Rotter S, Diesmann M (1999). Exact simulation of timeinvariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381402. DOI: https://doi.org/10.1007/s004220050570
 5
Roth A and van Rossum M (2010). Chapter 6: Modeling synapses. in De Schutter, Computational Modeling Methods for Neuroscientists, MIT Press.
Author: Daniel Naoumenko (modified iaf_cond_alpha by Schrader, Plesser)
SeeAlso: iaf_cond_exp, iaf_cond_alpha, iaf_cond_alpha_mc

class
iaf_cond_exp
: public Archiving_Node  #include <iaf_cond_exp.h>
Name: iaf_cond_exp  Simple conductance based leaky integrateandfire neuron model.
Description:
iaf_cond_exp is an implementation of a spiking neuron using IAF dynamics with conductancebased synapses. Incoming spike events induce a postsynaptic change of conductance modelled by an exponential function. The exponential function is normalised such that an event of weight 1.0 results in a peak conductance of 1 nS.
Parameters:
The following parameters can be set in the status dictionary.
V_m
mV
Membrane potential
E_L
mV
Leak reversal potential
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_th
mV
Spike threshold
V_reset
mV
Reset potential of the membrane
E_ex
mV
Excitatory reversal potential
E_in
mV
Inhibitory reversal potential
g_L
nS
Leak conductance
tau_syn_ex
ms
Rise time of the excitatory synaptic alpha function
tau_syn_in
ms
Rise time of the inhibitory synaptic alpha function
I_e
pA
Constant input current
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
References:
 1
Meffin H, Burkitt AN, Grayden DB (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. Journal of Computational Neuroscience, 16:159175. DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81
Author: Sven Schrader
SeeAlso: iaf_psc_delta, iaf_psc_exp, iaf_cond_exp

class
iaf_cond_exp_sfa_rr
: public Archiving_Node  #include <iaf_cond_exp_sfa_rr.h>
Name: iaf_cond_exp_sfa_rr  Simple conductance based leaky integrateandfire neuron model.
Description:
iaf_cond_exp_sfa_rr is an iaf_cond_exp_sfa_rr i.e. an implementation of a spiking neuron using IAF dynamics with conductancebased synapses, with additional spikefrequency adaptation and relative refractory mechanisms as described in Dayan+Abbott, 2001, page 166.
As for the iaf_cond_exp_sfa_rr, Incoming spike events induce a postsynaptic change of conductance modelled by an exponential function. The exponential function is normalised such that an event of weight 1.0 results in a peak current of 1 nS.
Outgoing spike events induce a change of the adaptation and relative refractory conductances by q_sfa and q_rr, respectively. Otherwise these conductances decay exponentially with time constants tau_sfa and tau_rr, respectively.
Parameters:
The following parameters can be set in the status dictionary.
V_m
mV
Membrane potential
E_L
mV
Leak reversal potential
C_m
pF
Capacity of the membrane
t_ref
ms
Duration of refractory period
V_th
mV
Spike threshold
V_reset
mV
Reset potential of the membrane
E_ex
mV
Excitatory reversal potential
E_in
mV
Inhibitory reversal potential
g_L
nS
Leak conductance
tau_syn_ex
ms
Rise time of the excitatory synaptic alpha function
tau_syn_in
ms
Rise time of the inhibitory synaptic alpha function
q_sfa
nS
Outgoing spike activated quantal spikefrequency adaptation conductance increase in nS
q_rr
nS
Outgoing spike activated quantal relative refractory conductance increase in nS
tau_sfa
ms
Time constant of spikefrequency adaptation in ms
tau_rr
ms
Time constant of the relative refractory mechanism in ms
E_sfa
mV
Spikefrequency adaptation conductance reversal potential in mV
E_rr
mV
Relative refractory mechanism conductance reversal potential in mV
I_e
pA
Constant input current
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
References:
 1
Meffin H, Burkitt AN, Grayden DB (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. Journal of Computational Neuroscience, 16:159175. DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81
 2
Dayan P, Abbott LF (2001). Theoretical neuroscience: Computational and mathematical modeling of neural systems. Cambridge, MA: MIT Press. https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=
item_3006127
Author: Sven Schrader, Eilif Muller
SeeAlso: iaf_cond_exp_sfa_rr, aeif_cond_alpha, iaf_psc_delta, iaf_psc_exp, iaf_cond_alpha

class
iaf_psc_alpha
: public Archiving_Node  #include <iaf_psc_alpha.h>
Name: iaf_psc_alpha  Leaky integrateandfire neuron model.
Description:
iaf_psc_alpha is an implementation of a leaky integrateandfire model with alphafunction shaped synaptic currents. Thus, synaptic currents and the resulting postsynaptic potentials have a finite rise time.
The threshold crossing is followed by an absolute refractory period during which the membrane potential is clamped to the resting potential.
The linear subthresold dynamics is integrated by the Exact Integration scheme [][1]. The neuron dynamics is solved on the time grid given by the computation step size. Incoming as well as emitted spikes are forced to that grid.
An additional state variable and the corresponding differential equation represents a piecewise constant external current.
The general framework for the consistent formulation of systems with neuron like dynamics interacting by point events is described in [1]. A flow chart can be found in [2].
Critical tests for the formulation of the neuron model are the comparisons of simulation results for different computation step sizes. sli/testsuite/nest contains a number of such tests.
The iaf_psc_alpha is the standard model used to check the consistency of the nest simulation kernel because it is at the same time complex enough to exhibit nontrivial dynamics and simple enough compute relevant measures analytically.
Remarks:
The present implementation uses individual variables for the components of the state vector and the nonzero matrix elements of the propagator. Because the propagator is a lower triangular matrix no full matrix multiplication needs to be carried out and the computation can be done “in place” i.e. no temporary state vector object is required.
The template support of recent C++ compilers enables a more succinct formulation without loss of runtime performance already at minimal optimization levels. A future version of iaf_psc_alpha will probably address the problem of efficient usage of appropriate vector and matrix objects.
Parameters:
The following parameters can be set in the status dictionary.
V_m
mV
Membrane potential
E_L
mV
Resting membrane potenial
C_m
pF
Capacity of the membrane
tau_m
ms
Membrane time constant
t_ref
ms
Duration of refractory period
V_th
mV
Spike threshold
V_reset
mV
Reset potential of the membrane
tau_syn_ex
ms
Rise time of the excitatory synaptic alpha function
tau_syn_in
ms
Rise time of the inhibitory synaptic alpha function
I_e
pA
Constant input current
V_min
mV
Absolute lower value for the membrane potenial
If tau_m is very close to tau_syn_ex or tau_syn_in, the model will numerically behave as if tau_m is equal to tau_syn_ex or tau_syn_in, respectively, to avoid numerical instabilities. For details, please see IAF_neurons_singularity.ipynb in the NEST source code (docs/model_details).
References:
 1
Rotter S, Diesmann M (1999). Exact simulation of timeinvariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381402. DOI: https://doi.org/10.1007/s004220050570
 2
Diesmann M, Gewaltig MO, Rotter S, & Aertsen A (2001). State space analysis of synchronous spiking in cortical neural networks. Neurocomputing 3840:565571. DOI: https://doi.org/10.1016/S09252312(01)00409X
 3
Morrison A, Straube S, Plesser H E, Diesmann M (2006). Exact subthreshold integration with continuous spike times in discrete time neural network simulations. Neural Computation, in press DOI: https://doi.org/10.1162/neco.2007.19.1.47
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
FirstVersion: September 1999
Author: Diesmann, Gewaltig
SeeAlso: iaf_psc_delta, iaf_psc_exp, iaf_cond_exp

class
iaf_psc_alpha_multisynapse
: public Archiving_Node  #include <iaf_psc_alpha_multisynapse.h>
Name: iaf_psc_alpha_multisynapse  Leaky integrateandfire neuron model with multiple ports.
Description:
iaf_psc_alpha_multisynapse is a direct extension of iaf_psc_alpha. On the postsynapic side, there can be arbitrarily many synaptic time constants (iaf_psc_alpha has exactly two: tau_syn_ex and tau_syn_in).
This can be reached by specifying separate receptor ports, each for a different time constant. The port number has to match the respective “receptor_type” in the connectors.
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Author: Schrader, adapted from iaf_psc_alpha
SeeAlso: iaf_psc_alpha, iaf_psc_delta, iaf_psc_exp, iaf_cond_exp, iaf_psc_exp_multisynapse

class
iaf_psc_delta
: public Archiving_Node  #include <iaf_psc_delta.h>
Name: iaf_psc_delta  Leaky integrateandfire neuron model.
Description:
iaf_psc_delta is an implementation of a leaky integrateandfire model where the potential jumps on each spike arrival.
The threshold crossing is followed by an absolute refractory period during which the membrane potential is clamped to the resting potential.
Spikes arriving while the neuron is refractory, are discarded by default. If the property “refractory_input” is set to true, such spikes are added to the membrane potential at the end of the refractory period, dampened according to the interval between arrival and end of refractoriness.
The linear subthresold dynamics is integrated by the Exact Integration scheme [1]. The neuron dynamics is solved on the time grid given by the computation step size. Incoming as well as emitted spikes are forced to that grid.
An additional state variable and the corresponding differential equation represents a piecewise constant external current.
The general framework for the consistent formulation of systems with neuron like dynamics interacting by point events is described in [1]. A flow chart can be found in [2].
Critical tests for the formulation of the neuron model are the comparisons of simulation results for different computation step sizes. sli/testsuite/nest contains a number of such tests.
The iaf_psc_delta is the standard model used to check the consistency of the nest simulation kernel because it is at the same time complex enough to exhibit nontrivial dynamics and simple enough compute relevant measures analytically.
Remarks:
The present implementation uses individual variables for the components of the state vector and the nonzero matrix elements of the propagator. Because the propagator is a lower triangular matrix no full matrix multiplication needs to be carried out and the computation can be done “in place” i.e. no temporary state vector object is required.
The template support of recent C++ compilers enables a more succinct formulation without loss of runtime performance already at minimal optimization levels. A future version of iaf_psc_delta will probably address the problem of efficient usage of appropriate vector and matrix objects.
Parameters:
The following parameters can be set in the status dictionary.
V_m
mV
Membrane potential
E_L
mV
Resting membrane potential
C_m
pF
Capacity of the membrane
tau_m
ms
Membrane time constant
t_ref
ms
Duration of refractory period
V_th
mV
Spike threshold
V_reset
mV
Reset potential of the membrane
I_e
pA
Constant input current
V_min
mV
Absolute lower value for the membrane potenial
refractory_input
boolean
If true, do not discard input during refractory period. Default: false
References:
 1
Rotter S, Diesmann M (1999). Exact simulation of timeinvariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381402. DOI: https://doi.org/10.1007/s004220050570
 2
Diesmann M, Gewaltig MO, Rotter S, & Aertsen A (2001). State space analysis of synchronous spiking in cortical neural networks. Neurocomputing 3840:565571. DOI: https://doi.org/10.1016/S09252312(01)00409X
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Author: September 1999, Diesmann, Gewaltig
SeeAlso: iaf_psc_alpha, iaf_psc_exp, iaf_psc_delta_ps

class
iaf_psc_exp
: public Archiving_Node  #include <iaf_psc_exp.h>
Name: iaf_psc_exp  Leaky integrateandfire neuron model with exponential PSCs.
Description:
iaf_psc_exp is an implementation of a leaky integrateandfire model with exponential shaped postsynaptic currents (PSCs) according to [1]. Thus, postsynaptic currents have an infinitely short rise time.
The threshold crossing is followed by an absolute refractory period (t_ref) during which the membrane potential is clamped to the resting potential and spiking is prohibited.
The linear subthresold dynamics is integrated by the Exact Integration scheme [2]. The neuron dynamics is solved on the time grid given by the computation step size. Incoming as well as emitted spikes are forced to that grid.
An additional state variable and the corresponding differential equation represents a piecewise constant external current.
The general framework for the consistent formulation of systems with neuron like dynamics interacting by point events is described in [2]. A flow chart can be found in [3].
Spiking in this model can be either deterministic (delta=0) or stochastic (delta model with escape noise [4, 5].
Remarks:
The present implementation uses individual variables for the components of the state vector and the nonzero matrix elements of the propagator. Because the propagator is a lower triangular matrix no full matrix multiplication needs to be carried out and the computation can be done “in place” i.e. no temporary state vector object is required.
The template support of recent C++ compilers enables a more succinct formulation without loss of runtime performance already at minimal optimization levels. A future version of iaf_psc_exp will probably address the problem of efficient usage of appropriate vector and matrix objects.
Parameters:
The following parameters can be set in the status dictionary.
E_L
mV
Resting membrane potential
C_m
pF
Capacity of the membrane
tau_m
ms
Membrane time constant
tau_syn_ex
ms
Time constant of postsynaptic excitatory currents
tau_syn_in
ms
Time constant of postsynaptic inhibitory currents
t_ref
ms
Duration of refractory period (V_m = V_reset)
V_m
mV
Membrane potential in mV
V_th
mV
Spike threshold in mV
V_reset
mV
Reset membrane potential after a spike
I_e
pA
Constant input current
t_spike
ms
Point in time of last spike
Remarks:
If tau_m is very close to tau_syn_ex or tau_syn_in, the model will numerically behave as if tau_m is equal to tau_syn_ex or tau_syn_in, respectively, to avoid numerical instabilities. For details, please see IAF_neurons_singularity.ipynb in the NEST source code (docs/model_details).
iaf_psc_exp can handle current input in two ways: Current input through receptor_type 0 are handled as stepwise constant current input as in other iaf models, i.e., this current directly enters the membrane potential equation. Current input through receptor_type 1, in contrast, is filtered through an exponential kernel with the time constant of the excitatory synapse, tau_syn_ex. For an example application, see [6].
References:
 1
Tsodyks M, Uziel A, Markram H (2000). Synchrony generation in recurrent networks with frequencydependent synapses. The Journal of Neuroscience, 20,RC50:15. URL: https://infoscience.epfl.ch/record/183402
 2
Rotter S, Diesmann M (1999). Exact simulation of timeinvariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381402. DOI: https://doi.org/10.1007/s004220050570
 3
Diesmann M, Gewaltig MO, Rotter S, & Aertsen A (2001). State space analysis of synchronous spiking in cortical neural networks. Neurocomputing 3840:565571. DOI: https://doi.org/10.1016/S09252312(01)00409X
 4
Schuecker J, Diesmann M, Helias M (2015). Modulated escape from a metastable state driven by colored noise. Physical Review E 92:052119 DOI: https://doi.org/10.1103/PhysRevE.92.052119
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
SeeAlso: iaf_psc_exp_ps
FirstVersion: March 2006
Author: Moritz Helias

class
iaf_psc_exp_multisynapse
: public Archiving_Node  #include <iaf_psc_exp_multisynapse.h>
psc
Name: iaf_psc_exp_multisynapse  Leaky integrateandfire neuron model with multiple ports.
Description:
iaf_psc_exp_multisynapse is a direct extension of iaf_psc_exp. On the postsynapic side, there can be arbitrarily many synaptic time constants (iaf_psc_exp has exactly two: tau_syn_ex and tau_syn_in).
This can be reached by specifying separate receptor ports, each for a different time constant. The port number has to match the respective “receptor_type” in the connectors.
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Author: Plesser, adapted from iaf_psc_alpha_multisynapse
SeeAlso: iaf_psc_alpha, iaf_psc_delta, iaf_psc_exp, iaf_cond_exp, iaf_psc_alpha_multisynapse

class
iaf_tum_2000
: public Archiving_Node  #include <iaf_tum_2000.h>
Name: iaf_tum_2000  Leaky integrateandfire neuron model with exponential PSCs.
Description:
iaf_tum_2000 is an implementation of a leaky integrateandfire model with exponential shaped postsynaptic currents (PSCs) according to [1]. The postsynaptic currents have an infinitely short rise time. In particular, this model allows setting an absolute and relative refractory time separately, as required by [1].
The threshold crossing is followed by an absolute refractory period (t_ref_abs) during which the membrane potential is clamped to the resting potential. During the total refractory period (t_ref_tot), the membrane potential evolves, but the neuron will not emit a spike, even if the membrane potential reaches threshold. The total refractory time must be larger or equal to the absolute refractory time. If equal, the refractoriness of the model if equivalent to the other models of NEST.
The linear subthreshold dynamics is integrated by the Exact Integration scheme [2]. The neuron dynamics is solved on the time grid given by the computation step size. Incoming as well as emitted spikes are forced to that grid.
An additional state variable and the corresponding differential equation represents a piecewise constant external current.
The general framework for the consistent formulation of systems with neuron like dynamics interacting by point events is described in [2]. A flow chart can be found in [3].
Remarks:
The present implementation uses individual variables for the components of the state vector and the nonzero matrix elements of the propagator. Because the propagator is a lower triangular matrix no full matrix multiplication needs to be carried out and the computation can be done “in place” i.e. no temporary state vector object is required.
The template support of recent C++ compilers enables a more succinct formulation without loss of runtime performance already at minimal optimization levels. A future version of iaf_tum_2000 will probably address the problem of efficient usage of appropriate vector and matrix objects.
Parameters:
The following parameters can be set in the status dictionary.
E_L
mV
Resting membrane potenial
C_m
pF
Capacity of the membrane
tau_m
ms
Membrane time constant
tau_syn_ex
ms
Time constant of postsynaptic excitatory currents
tau_syn_in
ms
Time constant of postsynaptic inhibitory currents
t_ref_abs
ms
Duration of absolute refractory period (V_m = V_reset)
t_ref_tot
ms
Duration of total refractory period (no spiking)
V_m
mV
Membrane potential
V_th
mV
Spike threshold
V_reset
mV
Reset membrane potential after a spike
I_e
pA
Constant input current
t_spike
ms
Point in time of last spike
Remarks:
If tau_m is very close to tau_syn_ex or tau_syn_in, the model will numerically behave as if tau_m is equal to tau_syn_ex or tau_syn_in, respectively, to avoid numerical instabilities. For details, please see IAF_neurons_singularity.ipynb in the NEST source code (docs/model_details).
References:
 1
Tsodyks M, Uziel A, Markram H (2000). Synchrony generation in recurrent networks with frequencydependent synapses. The Journal of Neuroscience, 20,RC50:15. URL: https://infoscience.epfl.ch/record/183402
 2
Rotter S, Diesmann M (1999). Exact simulation of timeinvariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381402. DOI: https://doi.org/10.1007/s004220050570
 3
Diesmann M, Gewaltig MO, Rotter S, & Aertsen A (2001). State space analysis of synchronous spiking in cortical neural networks. Neurocomputing 3840:565571. DOI: https://doi.org/10.1016/S09252312(01)00409X
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
FirstVersion: March 2006
Author: Moritz Helias

class
izhikevich
: public Archiving_Node  #include <izhikevich.h>
Name: izhikevich  Izhikevich neuron model
Description: Implementation of the simple spiking neuron model introduced by Izhikevich [1]. The dynamics are given by:
\[\begin{split} dv/dt = 0.04*v^2 + 5*v + 140  u + I \\ du/dt = a*(b*v  u)] \end{split}\]if \( v >= V_{th} \): v is set to c u is incremented by d
v jumps on each spike arrival by the weight of the spike.
As published in [1], the numerics differs from the standard forward Euler technique in two ways: 1) the new value of u is calculated based on the new value of v, rather than the previous value 2) the variable v is updated using a time step half the size of that used to update variable u.
This model offers both forms of integration, they can be selected using the boolean parameter consistent_integration. To reproduce some results published on the basis of this model, it is necessary to use the published form of the dynamics. In this case, consistent_integration must be set to false. For all other purposes, it is recommended to use the standard technique for forward Euler integration. In this case, consistent_integration must be set to true (default).
Parameters: The following parameters can be set in the status dictionary.
V_m
mV
Membrane potential
U_m
mV
Membrane potential recovery variable
V_th
mV
Spike threshold
I_e
pA
Constant input current (R=1)
V_min
mV
Absolute lower value for the membrane potential
a
real
Describes time scale of recovery variable
b
real
Sensitivity of recovery variable
c
mV
Afterspike reset value of V_m
d
mV
Afterspike reset value of U_m
consistent_integration
boolean
Use standard integration technique
References:
 1
Izhikevich EM (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks, 14:15691572. DOI: https://doi.org/10.1109/TNN.2003.820440
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
FirstVersion: 2009
Author: Hanuschkin, Morrison, Kunkel
SeeAlso: iaf_psc_delta, mat2_psc_exp

class
nonlinearities_lin_rate
¶  #include <lin_rate.h>
Name: lin_rate  Linear rate model
Description:
lin_rate is an implementation of a linear rate model with input function \( input(h) = g * h \). The model supports multiplicative coupling which can be switched on and off via the boolean parameter mult_coupling (default=false). In case multiplicative coupling is actived the excitatory input of the model is multiplied with the function \( mult\_coupling\_ex(rate) = g_{ex} * ( \theta_{ex}  rate ) \) and the inhibitory input is multiplied with the function \( mult\_coupling\_in(rate) = g_{in} * ( \theta_{in} + rate ) \).
The model supports connections to other rate models with either zero or nonzero delay, and uses the secondary_event concept introduced with the gapjunction framework.
Parameters:
The following parameters can be set in the status dictionary.
rate
real
Rate (unitless)
tau
ms
Time constant of rate dynamics
lambda
real
Passive decay rate
mu
real
Mean input
sigma
real
Noise parameter
g
real
Gain parameter
mult_coupling
boolean
Switch to enable/disable multiplicative coupling
g_ex
real
Linear factor in multiplicative coupling
g_in
real
Linear factor in multiplicative coupling
theta_ex
real
Shift in multiplicative coupling
theta_in
real
Shift in multiplicative coupling
rectify_output
boolean
Switch to restrict rate to values >= 0
References:
 1
Hahne J, Dahmen D, Schuecker J, Frommer A, Bolten M, Helias M, Diesmann M (2017). Integration of continuoustime dynamics in a spiking neural network simulator. Frontiers in Neuroinformatics, 11:34. DOI: https://doi.org/10.3389/fninf.2017.00034
 2
Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M (2015). A unified framework for spiking and gapjunction interactions in distributed neuronal network simulations. Frontiers Neuroinformatics, 9:22. DOI: https://doi.org/10.3389/fninf.2015.00022
Sends: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent
Receives: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent, DataLoggingRequest
Author: David Dahmen, Jan Hahne, Jannis Schuecker
SeeAlso: rate_connection_instantaneous, rate_connection_delayed

class
mat2_psc_exp
: public Archiving_Node  #include <mat2_psc_exp.h>
Name: mat2_psc_exp  Nonresetting leaky integrateandfire neuron model with exponential PSCs and adaptive threshold.
Description:
mat2_psc_exp is an implementation of a leaky integrateandfire model with exponential shaped postsynaptic currents (PSCs). Thus, postsynaptic currents have an infinitely short rise time.
The threshold is lifted when the neuron is fired and then decreases in a fixed time scale toward a fixed level [3].
The threshold crossing is followed by a total refractory period during which the neuron is not allowed to fire, even if the membrane potential exceeds the threshold. The membrane potential is NOT reset, but continuously integrated.
The linear subthresold dynamics is integrated by the Exact Integration scheme [1]. The neuron dynamics is solved on the time grid given by the computation step size. Incoming as well as emitted spikes are forced to that grid.
An additional state variable and the corresponding differential equation represents a piecewise constant external current.
The general framework for the consistent formulation of systems with neuron like dynamics interacting by point events is described in [1]. A flow chart can be found in [2].
Remarks:
The present implementation uses individual variables for the components of the state vector and the nonzero matrix elements of the propagator. Because the propagator is a lower triangular matrix no full matrix multiplication needs to be carried out and the computation can be done “in place” i.e. no temporary state vector object is required.
Parameters:
The following parameters can be set in the status dictionary:
C_m
pF
Capacity of the membrane
E_L
mV
Resting potential
tau_m
ms
Membrane time constant
tau_syn_ex
ms
Time constant of postsynaptic excitatory currents
tau_syn_in
ms
Time constant of postsynaptic inhibitory currents
t_ref
ms
Duration of absolute refractory period (no spiking)
V_m
mV
Membrane potential
I_e
pA
Constant input current
t_spike
ms
Point in time of last spike
tau_1
ms
Short time constant of adaptive threshold
tau_2
ms
Long time constant of adaptive threshold
alpha_1
mV
Amplitude of short time threshold adaption [3]
alpha_2
mV
Amplitude of long time threshold adaption [3]
omega
mV
Resting spike threshold (absolute value, not relative to E_L as in [3])
The following state variables can be read out with the multimeter device:
V_m
mV
Nonresetting membrane potential
V_th
mV
Twotimescale adaptive threshold
Remarks:
tau_m != tau_syn_{ex,in} is required by the current implementation to avoid a degenerate case of the ODE describing the model [1]. For very similar values, numerics will be unstable.
References:
 1
Rotter S and Diesmann M (1999). Exact simulation of timeinvariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381402. DOI: https://doi.org/10.1007/s004220050570
 2
Diesmann M, Gewaltig MO, Rotter S, Aertsen A (2001). State space analysis of synchronous spiking in cortical neural networks. Neurocomputing 3840:565571. DOI:https://doi.org/10.1016/S09252312(01)00409X
 3
Kobayashi R, Tsubo Y and Shinomoto S (2009). Madetoorder spiking neuron model equipped with a multitimescale adaptive threshold. Frontiers in Computuational Neuroscience 3:9. DOI: https://doi.org/10.3389/neuro.10.009.2009
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
FirstVersion: Mai 2009
Author: Thomas Pfeil (modified iaf_psc_exp model of Moritz Helias)

class
gainfunction_mcculloch_pitts
 #include <mcculloch_pitts_neuron.h>
Name: mcculloch_pitts_neuron  Binary deterministic neuron with Heaviside activation function.
Description:
The mcculloch_pitts_neuron is an implementation of a binary neuron that is irregularly updated as Poisson time points [1]. At each update point the total synaptic input h into the neuron is summed up, passed through a Heaviside gain function g(h) = H(htheta), whose output is either 1 (if input is above) or 0 (if input is below threshold theta). The time constant tau_m is defined as the mean interupdateinterval that is drawn from an exponential distribution with this parameter. Using this neuron to reprodce simulations with asynchronous update [1], the time constant needs to be chosen as tau_m = dt*N, where dt is the simulation time step and N the number of neurons in the original simulation with asynchronous update. This ensures that a neuron is updated on average every tau_m ms. Since in the original paper [1] neurons are coupled with zero delay, this implementation follows this definition. It uses the update scheme described in [3] to maintain causality: The incoming events in time step t_i are taken into account at the beginning of the time step to calculate the gain function and to decide upon a transition. In order to obtain delayed coupling with delay d, the user has to specify the delay d+h upon connection, where h is the simulation time step.
Remarks:
This neuron has a special use for spike events to convey the binary state of the neuron to the target. The neuron model only sends a spike if a transition of its state occurs. If the state makes an uptransition it sends a spike with multiplicity 2, if a down transition occurs, it sends a spike with multiplicity 1. The decoding scheme relies on the feature that spikes with multiplicity larger 1 are delivered consecutively, also in a parallel setting. The creation of double connections between binary neurons will destroy the decoding scheme, as this effectively duplicates every event. Using random connection routines it is therefore advisable to set the property ‘multapses’ to false. The neuron accepts several sources of currents, e.g. from a noise_generator.
Parameters:
tau_m
ms
Membrane time constant (mean interupdateinterval)
theta
mV
Threshold for sigmoidal activation function
References:
 1
McCulloch W, Pitts W (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5:115133. DOI: https://doi.org/10.1007/BF02478259
 2
Hertz J, Krogh A, Palmer R (1991). Introduction to the theory of neural computation. AddisonWesley Publishing Conmpany.
 3
Morrison A, Diesmann M (2007). Maintaining causality in discrete time neuronal simulations. In: Lectures in Supercomputational Neuroscience, p. 267. Peter beim Graben, Changsong Zhou, Marco Thiel, Juergen Kurths (Eds.), Springer. DOI: https://doi.org/10.1007/9783540731597_10
Sends: SpikeEvent
Receives: SpikeEvent, PotentialRequest
FirstVersion: February 2013
Author: Moritz Helias
SeeAlso: pp_psc_delta

class
parrot_neuron
: public Archiving_Node¶  #include <parrot_neuron.h>
Name: parrot_neuron  Neuron that repeats incoming spikes.
Description:
The parrot neuron simply emits one spike for every incoming spike. An important application is to provide identical poisson spike trains to a group of neurons. The poisson_generator sends a different spike train to each of its target neurons. By connecting one poisson_generator to a parrot_neuron and then that parrot_neuron to a group of neurons, all target neurons will receive the same poisson spike train.
Remarks:
Weights on connection to the parrot_neuron are ignored.
Weights on connections from the parrot_neuron are handled as usual.
Delays are honored on incoming and outgoing connections.
Multiplicity may be used to indicate number of spikes in a single time step. Instead of the accumulated weigths of the incoming spikes, the number of the spikes is stored within a ring buffer.
Only spikes arriving on connections to port 0 will be repeated. Connections onto port 1 will be accepted, but spikes incoming through port 1 will be ignored. This allows setting exact pre and postsynaptic spike times for STDP protocols by connecting two parrot neurons spiking at desired times by, e.g., a stdp_synapse onto port 1 on the postsynaptic parrot neuron.
Receives: SpikeEvent
Sends: SpikeEvent
Parameters:
No parameters to be set in the status dictionary.
Author: David Reichert, Abigail Morrison, Alexander Seeholzer, Hans Ekkehard Plesser
FirstVersion: May 2006

class
pp_pop_psc_delta
: public Node  #include <pp_pop_psc_delta.h>
Name: pp_pop_psc_delta  Population of point process neurons with leaky integration of deltashaped PSCs.
Description:
pp_pop_psc_delta is an effective model of a population of neurons. The N component neurons are assumed to be spike response models with escape noise, also known as generalized linear models. We follow closely the nomenclature of [1]. The component neurons are a special case of pp_psc_delta (with purely exponential rate function, no reset and no random dead_time). All neurons in the population share the inputs that it receives, and the output is the pooled spike train.
The instantaneous firing rate of the N component neurons is defined as
\[ rate(t) = \rho_0 * \exp( (h(t)  \eta(t))/\delta_u ), \]where h(t) is the input potential (synaptic delta currents convolved with an exponential kernel with time constant tau_m), eta(t) models the effect of refractoriness and adaptation (the neuron’s own spike train convolved with a sum of exponential kernels with time constants tau_eta), and delta_u sets the scale of the voltages.
To represent a (homogeneous) population of N inhomogeneous renewal process neurons, we can keep track of the numbers of neurons that fired a certain number of time steps in the past. These neurons will have the same value of the hazard function (instantaneous rate), and we draw a binomial random number for each of these groups. This algorithm is thus very similar to ppd_sup_generator and gamma_sup_generator, see also [2].
However, the adapting threshold eta(t) of the neurons generally makes the neurons nonrenewal processes. We employ the quasirenewal approximation [1], to be able to use the above algorithm. For the extension of [1] to coupled populations see [3].
In effect, in each simulation time step, a binomial random number for each of the groups of neurons has to be drawn, independent of the number of represented neurons. For large N, it should be much more efficient than simulating N individual pp_psc_delta models.
pp_pop_psc_delta emits spike events like other neuron models, but no more than one per time step. If several component neurons spike in the time step, the multiplicity of the spike event is set accordingly. Thus, to monitor its output, the multiplicity of the spike events has to be taken into account. Alternatively, the internal variable n_events gives the number of spikes emitted in a time step, and can be monitored using a multimeter.
EDIT Nov 2016: pp_pop_psc_delta is now deprecated, because a new and presumably much faster population model implementation is now available, see gif_pop_psc_exp.
Parameters:
The following parameters can be set in the status dictionary.
N
integer
Number of represented neurons
tau_m
ms
Membrane time constant
C_m
pF
Capacitance of the membrane
rho_0
1/s
Base firing rate
delta_u
mV
Voltage scale parameter
I_e
pA
Constant input current
tau_eta
list of ms
Time constants of postspike kernel
val_eta
list of mV
Amplitudes of exponentials in postspikekernel
len_kernel
real
Postspike kernel eta is truncated after max(tau_eta) * len_kernel
The parameters correspond to the ones of pp_psc_delta as follows.
c_1
0.0
c_2
rho_0
c_3
1/delta_u
q_sfa
val_eta
tau_sfa
tau_eta
I_e
I_e
dead_time
simulation resolution
dead_time_random
False
with_reset
False
t_ref_remaining
0.0
References:
 1
Naud R, Gerstner W (2012). Coding and decoding with adapting neurons: a population approach to the peristimulus time histogram. PLoS Compututational Biology 8: e1002711. DOI: https://doi.org/10.1371/journal.pcbi.1002711
 2
Deger M, Helias M, Boucsein C, Rotter S (2012). Statistical properties of superimposed stationary spike trains. Journal of Computational Neuroscience 32:3, 443463. DOI: https://doi.org/10.1007/s1082701103628
 3
Deger M, Schwalger T, Naud R, Gerstner W (2014). Fluctuations and information filtering in coupled populations of spiking neurons with adaptation. Physical Review E 90:6, 062704. DOI: https://doi.org/10.1103/PhysRevE.90.062704
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Author: May 2014, Setareh, Deger
SeeAlso: gif_pop_psc_exp, pp_psc_delta, ppd_sup_generator, gamma_sup_generator

class
pp_psc_delta
: public Archiving_Node  #include <pp_psc_delta.h>
Name: pp_psc_delta  Point process neuron with leaky integration of deltashaped PSCs.
Description:
pp_psc_delta is an implementation of a leaky integrator, where the potential jumps on each spike arrival. It produces spike stochastically, and supports spikefrequency adaptation, and other optional features.
Spikes are generated randomly according to the current value of the transfer function which operates on the membrane potential. Spike generation is followed by an optional dead time. Setting with_reset to true will reset the membrane potential after each spike.
The transfer function can be chosen to be linear, exponential or a sum of both by adjusting three parameters:
\[ rate = Rect[ c_1 * V' + c_2 * \exp(c_3 * V') ], \]where the effective potential \( V' = V_m  E_{sfa} \) and \( E_{sfa} \) is called the adaptive threshold. Here Rect means rectifier: \( Rect(x) = {x \text{ if } x>=0, 0 \text{ else}} \) (this is necessary because negative rates are not possible).
By setting c_3 = 0, c_2 can be used as an offset spike rate for an otherwise linear rate model.
The dead time enables to include refractoriness. If dead time is 0, the number of spikes in one time step might exceed one and is drawn from the Poisson distribution accordingly. Otherwise, the probability for a spike is given by \( 1  \exp(rate*h) \), where h is the simulation time step. If dead_time is smaller than the simulation resolution (time step), it is internally set to the resolution.
Note that, even if nonrefractory neurons are to be modeled, a small value of dead_time, like dead_time=1e8, might be the value of choice since it uses faster uniform random numbers than dead_time=0, which draws Poisson numbers. Only for very large spike rates (> 1 spike/time_step) this will cause errors.
The model can optionally include an adaptive firing threshold. If the neuron spikes, the threshold increases and the membrane potential will take longer to reach it. Here this is implemented by subtracting the value of the adaptive threshold E_sfa from the membrane potential V_m before passing the potential to the transfer function, see also above. E_sfa jumps by q_sfa when the neuron fires a spike, and decays exponentially with the time constant tau_sfa after (see [2] or [3]). Thus, the E_sfa corresponds to the convolution of the neuron’s spike train with an exponential kernel. This adaptation kernel may also be chosen as the sum of n exponential kernels. To use this feature, q_sfa and tau_sfa have to be given as a list of n values each.
The firing of pp_psc_delta is usually not a renewal process. For example, its firing may depend on its past spikes if it has nonzero adaptation terms (q_sfa). But if so, it will depend on all its previous spikes, not just the last one so it is not a renewal process model. However, if “with_reset” is True, and all adaptation terms (q_sfa) are 0, then it will reset (“forget”) its membrane potential each time a spike is emitted, which makes it a renewal process model (where “rate” above is its hazard function, also known as conditional intensity).
pp_psc_delta may also be called a spikeresponse model with escapenoise [6] (for vanishing, nonrandom dead_time). If c_1>0 and c_2==0, the rate is a convolution of the inputs with exponential filters which is a model known as a Hawkes point process (see [4]). If instead c_1==0, then pp_psc_delta is a point process generalized linear model (with the canonical link function, and exponential input filters) (see [5,6]).
This model has been adapted from iaf_psc_delta. The default parameters are set to the mean values given in [2], which have been matched to spiketrain recordings. Due to the many features of pp_psc_delta and its versatility, parameters should be set carefully and conciously.
Parameters:
The following parameters can be set in the status dictionary.
V_m
mV
Membrane potential
C_m
pF
Capacitance of the membrane
tau_m
ms
Membrane time constant
q_sfa
mV
Adaptive threshold jump
tau_sfa
ms
Adaptive threshold time constant
dead_time
ms
Duration of the dead time
dead_time_random
boolean
Should a random dead time be drawn after each spike?
dead_time_shape
integer
Shape parameter of dead time gamma distribution
t_ref_remaining
ms
Remaining dead time at simulation start
with_reset
boolean
Should the membrane potential be reset after a spike?
I_e
pA
Constant input current
c_1
Hz/mV
Slope of linear part of transfer function in Hz/mV
c_2
Hz
Prefactor of exponential part of transfer function
c_3
1/mV
Coefficient of exponential nonlinearity of transfer function
References:
 1
Cardanobile S, Rotter S (2010). Multiplicatively interacting point processes and applications to neural modeling. Journal of Computational Neuroscience 28(2):267284 DOI: https://doi.org/10.1007/s1082700902040
 2
Jolivet R, Rauch A, Luescher HR, Gerstner W. (2006). Predicting spike timing of neocortical pyramidal neurons by simple threshold models. Journal of Computational Neuroscience 21:3549. DOI: https://doi.org/10.1007/s1082700670745
 3
Pozzorini C, Naud R, Mensi S, Gerstner W (2013). Temporal whitening by powerlaw adaptation in neocortical neurons. Nature Neuroscience 16:942948. (Uses a similar model of multitimescale adaptation) DOI: https://doi.org/10.1038/nn.3431
 4
Grytskyy D, Tetzlaff T, Diesmann M, Helias M (2013). A unified view on weakly correlated recurrent networks. Frontiers in Computational Neuroscience, 7:131. DOI: https://doi.org/10.3389/fncom.2013.00131
 5
Deger M, Schwalger T, Naud R, Gerstner W (2014). Fluctuations and information filtering in coupled populations of spiking neurons with adaptation. Physical Review E 90:6, 062704. DOI: https://doi.org/10.1103/PhysRevE.90.062704
 6
Gerstner W, Kistler WM, Naud R, Paninski L (2014). Neuronal Dynamics: From single neurons to networks and models of cognition. Cambridge University Press
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Author: July 2009, Deger, Helias; January 2011, Zaytsev; May 2014, Setareh
SeeAlso: pp_pop_psc_delta, iaf_psc_delta, iaf_psc_alpha, iaf_psc_exp, iaf_psc_delta_ps

template<class
TNonlinearities
>
classrate_neuron_ipn
: public Archiving_Node¶  #include <rate_neuron_ipn.h>
Name: rate_neuron_ipn  Base class for rate model with input noise.
Description:
Base class for rate model with input noise of the form
\[ \tau dX_i(t) = [  \lambda X_i(t) + \mu + \phi( \sum w_{ij} \cdot \psi( X_j(td_{ij}) ) ) ] dt + [ \sqrt{\tau} \cdot \sigma ] dW_{i}(t) \]or\[\begin{split} \tau dX_i(t) = [  \lambda X_i(t) + \mu + \text{mult_coupling_ex}( X_i(t) ) \cdot \\ \phi( \sum w^{ > 0 }_{ij} \cdot \psi( X_j(td_{ij}) ) ) \\ + \text{mult_coupling_in}( X_i(t) ) \cdot \\ \phi( \sum w^{ < 0 }_{ij} \cdot \psi( X_j(td_{ij}) ) ) ] dt \\ + [ \sqrt{\tau} \cdot \sigma ] dW_{i}(t) \end{split}\]This template class needs to be instantiated with a class containing the following functions:input (nonlinearity that is applied to the input, either psi or phi)
mult_coupling_ex (factor of multiplicative coupling for excitatory input)
mult_coupling_in (factor of multiplicative coupling for inhibitory input)
The boolean parameter linear_summation determines whether the input function is applied to the summed up incoming connections (True, default value, input represents phi) or to each input individually (False, input represents psi). In case of multiplicative coupling the nonlinearity is applied separately to the summed excitatory and inhibitory inputs if linear_summation=True.
References:
 1
Hahne J, Dahmen D, Schuecker J, Frommer A, Bolten M, Helias M, Diesmann M (2017). Integration of continuoustime dynamics in a spiking neural network simulator. Frontiers in Neuroinformatics, 11:34. DOI: https://doi.org/10.3389/fninf.2017.00034
Author: David Dahmen, Jan Hahne, Jannis Schuecker
SeeAlso: lin_rate, tanh_rate, threshold_lin_rate

template<class
TNonlinearities
>
classrate_neuron_opn
: public Archiving_Node¶  #include <rate_neuron_opn.h>
Name: rate_neuron_opn  Base class for rate model with output noise.
Description:
Base class for rate model with output noise of the form
\[ \tau dX_i(t) / dt =  X_i(t) + \mu + \phi( \sum w_{ij} \cdot \psi( X_j(td_{ij}) + \sqrt{\tau} \cdot \sigma \cdot \xi_j(t) ) ) \]or\[\begin{split} \tau dX_i(t) / dt =  X_i(t) + \mu + \text{mult_coupling_ex}( X_i(t) ) \cdot \\ \phi( \sum w^{ > 0 }_{ij} \cdot \psi( X_j(td_{ij}) \\ + \sqrt{\tau} \cdot \sigma \cdot \xi_j(t) ) ) \\ + \text{mult_coupling_in}( X_i(t) ) \cdot \\ \phi( \sum w^{ < 0 }_{ij} \cdot \psi( X_j(td_{ij}) \\ + \sqrt{\tau} \cdot \sigma \cdot \xi_j(t) ) ) \end{split}\]Here \( xi_j(t) \) denotes a Gaussian white noise.
This template class needs to be instantiated with a class containing the following functions:
input (nonlinearity that is applied to the input, either psi or phi)
mult_coupling_ex (factor of multiplicative coupling for excitatory input)
mult_coupling_in (factor of multiplicative coupling for inhibitory input)
The boolean parameter linear_summation determines whether the input function is applied to the summed up incoming connections (True, default value, input represents phi) or to each input individually (False, input represents psi). In case of multiplicative coupling the nonlinearity is applied separately to the summed excitatory and inhibitory inputs if linear_summation=True.
References:
 1
Hahne J, Dahmen D, Schuecker J, Frommer A, Bolten M, Helias M, Diesmann M (2017). Integration of continuoustime dynamics in a spiking neural network simulator. Frontiers in Neuroinformatics, 11:34. DOI: https://doi.org./10.3389/fninf.2017.00034
Author: David Dahmen, Jan Hahne, Jannis Schuecker
SeeAlso: lin_rate, tanh_rate, threshold_lin_rate

template<class
TNonlinearities
>
classrate_transformer_node
: public Archiving_Node¶  #include <rate_transformer_node.h>
Name: rate_transformer_node  Rate neuron that sums up incoming rates and applies a nonlinearity specified via the template.
Description:
The rate transformer node simply applies the nonlinearity specified in the inputfunction of the template class to all incoming inputs. The boolean parameter linear_summation determines whether the input function is applied to the summed up incoming connections (True, default value) or to each input individually (False). An important application is to provide the possibility to apply different nonlinearities to different incoming connections of the same rate neuron by connecting the sending rate neurons to the rate transformer node and connecting the rate transformer node to the receiving rate neuron instead of using a direct connection. Please note that for instantaneous rate connections the rate arrives one time step later at the receiving rate neurons as with a direct connection.
Remarks:
Weights on connections from and to the rate_transformer_node are handled as usual.
Delays are honored on incoming and outgoing connections.
Receives: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent
Sends: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent
Parameters:
Only the parameter
linear_summation and the parameters from the class Nonlinearities can be set in the status dictionary.
Author: Mario Senden, Jan Hahne, Jannis Schuecker
FirstVersion: November 2017

class
siegert_neuron
: public Archiving_Node¶  #include <siegert_neuron.h>
Name: siegert_neuron
Description:
siegert_neuron is an implementation of a rate model with the nonlinearity given by the gain function of the leakyintegrateandfire neuron with delta or exponentially decaying synapses [2] and [3, their eq. 25]. The model can be used for a meanfield analysis of spiking networks.
The model supports connections to other rate models with zero delay, and uses the secondary_event concept introduced with the gapjunction framework.
Parameters:
The following parameters can be set in the status dictionary.
rate
1/s
Rate (1/s)
tau
ms
Time constant
mean
real
Additional constant input
The following parameters can be set in the status directory and are used in the evaluation of the gain function. Parameters as in iaf_psc_exp/delta.
tau_m
ms
Membrane time constant
tau_syn
ms
Time constant of postsynaptic currents
t_ref
ms
Duration of refractory period
theta
mV
Threshold relative to resting potential
V_reset
mV
Reset relative to resting membrane potential
References:
 1
Hahne J, Dahmen D, Schuecker J, Frommer A, Bolten M, Helias M, Diesmann M (2017). Integration of continuoustime dynamics in a spiking neural network simulator. Frontiers in Neuroinformatics, 11:34. DOI: https://doi.org/10.3389/fninf.2017.00034
 2
Fourcaud N, Brunel N (2002). Dynamics of the firing probability of noisy integrateandfire neurons, Neural Computation, 14(9):20572110 DOI: https://doi.org/10.1162/089976602320264015
 3
Schuecker J, Diesmann M, Helias M (2015). Modulated escape from a metastable state driven by colored noise. Physical Review E 92:052119 DOI: https://doi.org/10.1103/PhysRevE.92.052119
 4
Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M (2015). A unified framework for spiking and gapjunction interactions in distributed neuronal network simulations. Frontiers in Neuroinformatics, 9:22. DOI: https://doi.org/10.3389/fninf.2015.00022
Sends: DiffusionConnectionEvent
Receives: DiffusionConnectionEvent, DataLoggingRequest
Author: Jannis Schuecker, David Dahmen, Jan Hahne
SeeAlso: diffusion_connection

class
nonlinearities_sigmoid_rate
¶  #include <sigmoid_rate.h>
Name: sigmoid_rate  rate model with sigmoidal gain function
Description:
sigmoid_rate is an implementation of a nonlinear rate model with input function \( input(h) = g / ( 1. + \exp( \beta * ( h  \theta ) ) ) \). Input transformation can either be applied to individual inputs or to the sum of all inputs.
The model supports connections to other rate models with either zero or nonzero delay, and uses the secondary_event concept introduced with the gapjunction framework.
Parameters:
The following parameters can be set in the status dictionary.
rate
real
Rate (unitless)
tau
ms
Time constant of rate dynamics
mu
real
Mean input
sigma
real
Noise parameter
g
real
Gain parameter
beta
real
Slope parameter
theta
real
Threshold
linear_summation
boolean
Specifies type of nonlinearity (see above)
rectify_output
boolean
Switch to restrict rate to values >= 0
Note:
The boolean parameter linear_summation determines whether the input from different presynaptic neurons is first summed linearly and then transformed by a nonlinearity (true), or if the input from individual presynaptic neurons is first nonlinearly transformed and then summed up (false). Default is true.
References:
 1
Hahne J, Dahmen D, Schuecker J, Frommer A, Bolten M, Helias M, Diesmann M (2017). Integration of continuoustime dynamics in a spiking neural network simulator. Frontiers in Neuroinformatics, 11:34. DOI: https://doi.org/10.3389/fninf.2017.00034
 2
Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M (2015). A unified framework for spiking and gapjunction interactions in distributed neuronal network simulations. Frontiers in Neuroinformatics, 9:22. DOI: https://doi.org/10.3389/fninf.2015.00022
Sends: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent
Receives: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent, DataLoggingRequest
Author: Mario Senden, Jan Hahne, Jannis Schuecker
SeeAlso: rate_connection_instantaneous, rate_connection_delayed

class
nonlinearities_sigmoid_rate_gg_1998
¶  #include <sigmoid_rate_gg_1998.h>
Name: sigmoid_rate_gg_1998  rate model with sigmoidal gain function as defined in [1].
Description:
sigmoid_rate_gg_1998 is an implementation of a nonlinear rate model with input function \( input(h) = ( g * h )^4 / ( .1^4 + ( g * h )^4 ) \). Input transformation can either be applied to individual inputs or to the sum of all inputs.
The model supports connections to other rate models with either zero or nonzero delay, and uses the secondary_event concept introduced with the gapjunction framework.
Parameters:
The following parameters can be set in the status dictionary.
rate
real
Rate (unitless)
tau
ms
Time constant of rate dynamics
mu
real
Mean input
sigma
real
Noise parameter
g
real
Gain parameter
linear_summation
boolean
Specifies type of nonlinearity (see above)
rectify_output
boolean
Switch to restrict rate to values >= 0
Note:
The boolean parameter linear_summation determines whether the input from different presynaptic neurons is first summed linearly and then transformed by a nonlinearity (true), or if the input from individual presynaptic neurons is first nonlinearly transformed and then summed up (false). Default is true.
References:
 1
Gancarz G, Grossberg S (1998). A neural model of the saccade generator in the reticular formation. Neural Networks, 11(7):1159–1174. DOI: https://doi.org/10.1016/S08936080(98)000963
 2
Hahne J, Dahmen D, Schuecker J, Frommer A, Bolten M, Helias M, Diesmann M (2017). Integration of continuoustime dynamics in a spiking neural network simulator. Frontiers in Neuroinformatics, 11:34. DOI: https://doi.org/10.3389/fninf.2017.00034
 3
Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M (2015). A unified framework for spiking and gapjunction interactions in distributed neuronal network simulations. Frontiers in Neuroinformatics, 9:22. DOI: https://doi/org/10.3389/fninf.2015.00022
Sends: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent
Receives: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent, DataLoggingRequest
Author: Mario Senden, Jan Hahne, Jannis Schuecker
SeeAlso: rate_connection_instantaneous, rate_connection_delayed

class
nonlinearities_tanh_rate
¶  #include <tanh_rate.h>
Name: tanh_rate  rate model with hyperbolic tangent nonlinearity
Description:
tanh_rate is an implementation of a nonlinear rate model with input function \( input(h) = \tanh(g * (h\theta)) \). Input transformation can either be applied to individual inputs or to the sum of all inputs.
The model supports connections to other rate models with either zero or nonzero delay, and uses the secondary_event concept introduced with the gapjunction framework.
Parameters:
The following parameters can be set in the status dictionary.
rate
real
Rate (unitless)
tau
ms
Time constant of rate dynamics
mu
real
Mean input
sigma
real
Noise parameter
g
real
Gain parameter
theta
real
Threshold
linear_summation
boolean
Specifies type of nonlinearity (see above)
rectify_output
boolean
Switch to restrict rate to values >= 0
Note:
The boolean parameter linear_summation determines whether the input from different presynaptic neurons is first summed linearly and then transformed by a nonlinearity (true), or if the input from individual presynaptic neurons is first nonlinearly transformed and then summed up (false). Default is true.
References:
 1
Hahne J, Dahmen D, Schuecker J, Frommer A, Bolten M, Helias M, Diesmann M (2017). Integration of continuoustime dynamics in a spiking neural network simulator. Frontiers in Neuroinformatics, 11:34. DOI: https://doi.org/10.3389/fninf.2017.00034
 2
Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M (2015). A unified framework for spiking and gapjunction interactions in distributed neuronal network simulations. Frontiers in Neuroinformatics, 9:22. DOI: https://doi.org/10.3389/fninf.2015.00022
Sends: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent
Receives: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent, DataLoggingRequest
Author: David Dahmen, Jan Hahne, Jannis Schuecker
SeeAlso: rate_connection_instantaneous, rate_connection_delayed

class
nonlinearities_threshold_lin_rate
¶  #include <threshold_lin_rate.h>
Name: threshold_lin_rate  rate model with thresholdlinear gain function
Description:
threshold_lin_rate is an implementation of a nonlinear rate model with input function \( input(h) = min( max( g * ( h  \theta ), 0 ), \alpha ) \). Input transformation can either be applied to individual inputs or to the sum of all inputs.
The model supports connections to other rate models with either zero or nonzero delay, and uses the secondary_event concept introduced with the gapjunction framework.
Parameters:
The following parameters can be set in the status dictionary.
rate
real
Rate (unitless)
tau
ms
Time constant of rate dynamics
mu
real
Mean input
sigma
real
Noise parameter
g
real
Gain parameter
alpha
real
Second Threshold
theta
real
Threshold
linear_summation
boolean
Specifies type of nonlinearity (see above)
rectify_output
boolean
Switch to restrict rate to values >= 0
Note: The boolean parameter linear_summation determines whether the input from different presynaptic neurons is first summed linearly and then transformed by a nonlinearity (true), or if the input from individual presynaptic neurons is first nonlinearly transformed and then summed up (false). Default is true.
References:
 1
Hahne J, Dahmen D, Schuecker J, Frommer A, Bolten M, Helias M, Diesmann M (2017). Integration of continuoustime dynamics in a spiking neural network simulator. Frontiers in Neuroinformatics, 11:34. DOI: https://doi.org/10.3389/fninf.2017.00034
 2
Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M (2015). A unified framework for spiking and gapjunction interactions in distributed neuronal network simulations. Frontiers in Neuroinformatics, 9:22. DOI: https://doi.org/10.3389/fninf.2015.00022
Sends: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent
Receives: InstantaneousRateConnectionEvent, DelayedRateConnectionEvent, DataLoggingRequest
Author: David Dahmen, Jan Hahne, Jannis Schuecker SeeAlso: rate_connection_instantaneous, rate_connection_delayed