izhikevich – Izhikevich neuron model

Description

Implementation of the simple spiking neuron model introduced by Izhikevich 1. 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
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