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This is A PREVIEW for NEST 3.0 and NOT an OFFICIAL RELEASE! Some functionality may not be available and information may be incomplete!

aeif_cond_alpha – Conductance based exponential integrate-and-fire neuron model

Description

aeif_cond_alpha is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005). Synaptic conductances are modelled as alpha-functions.

This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with adaptive step size to integrate the differential equation.

The membrane potential is given by the following differential equation:

\[\begin{split}C_m \frac{dV}{dt} = -g_L(V-E_L)+g_L\Delta_T\exp\left(\frac{V-V_{th}}{\Delta_T}\right) - g_e(t)(V-E_e) \\ -g_i(t)(V-E_i)-w +I_e\end{split}\]

and

\[\tau_w \frac{dw}{dt} = a(V-E_L) - w\]

For implementation details see the aeif_models_implementation notebook.

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

Spike-adaptation 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

Spike-triggered 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.

Sends

SpikeEvent

Receives

SpikeEvent, CurrentEvent, DataLoggingRequest

References

1

Brette R and Gerstner W (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. Journal of Neurophysiology. 943637-3642 DOI: https://doi.org/10.1152/jn.00686.2005