Warning

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_psc_delta – Current-based adaptive exponential integrate-and-fire neuron model 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 Runge-Kutta-Fehlberg solver with adaptive stepsize to integrate the differential equation.

The membrane potential is given by the following differential equation:

\[\begin{split}C dV/dt= -g_L(V-E_L)+g_L*\Delta_T*\exp((V-V_T)/\Delta_T)-g_e(t)(V-E_e) \\ -g_i(t)(V-E_i)-w +I_e\end{split}\]

and

\[\tau_w * dw/dt= a(V-E_L) -W\]
\[I(t) = J \sum_k \delta(t - t^k).\]

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.

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

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

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.

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. J Neurophysiol 94:3637-3642. DOI: https://doi.org/10.1152/jn.00686.2005