izhikevich_psc_exp – Izhikevich neuron model with exponential postsynaptic currents

Description

Implementation of the simple spiking neuron model introduced by Izhikevich 1, with postsynaptic currents in the form of truncated exponentials. The dynamics are given by:

\[\begin{split}\frac{dV_m}{dt} &= 0.04 V_m^2 + 5 V_m + 140 - u + I \\ \frac{du}{dt} &= a (b V_m - u)\end{split}\]

\[\begin{split}&\text{if}\;\;\; V_m \geq V_{th}:\\ &\;\;\;\; V_m \text{ is set to } c\\ &\;\;\;\; u \text{ is incremented by } d\\ & \, \\ &v \text{ jumps on each spike arrival by the weight of the spike}\end{split}\]

This implementation uses the standard technique for forward Euler integration.

Parameters

The following parameters can be set in the status dictionary.

V_m	mV	Membrane potential
I_syn	pA	Synaptic current
u	mV	Membrane potential recovery variable
V_th	mV	Spike threshold
a	real	Describes time scale of recovery variable
b	real	Sensitivity of recovery variable
c	mV	After-spike reset value of V_m
d	mV	After-spike reset value of u
I_e	pA	Constant input current
t_ref	ms	Refractory time
tau_syn	ms	Time constant of synaptic current
den_delay	ms	Dendritic delay

References

1

Izhikevich EM (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks, 14:1569-1572. DOI: https://doi.org/10.1109/TNN.2003.820440