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