izhikevich
izhikevich - Izhikevich neuron model
Description
Implementation of the simple spiking neuron model introduced by Izhikevich [1]. The dynamics are given by:
Incoming spikes cause an instantaneous jump in the membrane potential proportional to the strength of the synapse.
As published in [1], the numerics differs from the standard forward Euler technique in two ways:
the new value of \(u\) is calculated based on the new value of \(v\), rather than the previous value
the variable \(v\) is updated using a time step half the size of that used to update variable \(u\).
This model will instead be simulated using the numerical solver that is recommended by ODE-toolbox during code generation.
References
Parameters
Name |
Physical unit |
Default value |
Description |
---|---|---|---|
a |
real |
0.02 |
describes time scale of recovery variable |
b |
real |
0.2 |
sensitivity of recovery variable |
c |
mV |
-65mV |
after-spike reset value of V_m |
d |
real |
8.0 |
after-spike reset value of U_m |
V_m_init |
mV |
-65mV |
initial membrane potential |
V_min |
mV |
-inf * mV |
Absolute lower value for the membrane potential. |
I_e |
pA |
0pA |
constant external input current |
State variables
Name |
Physical unit |
Default value |
Description |
---|---|---|---|
V_m |
mV |
V_m_init |
Membrane potential |
U_m |
real |
b * V_m_init |
Membrane potential recovery variable |
Equations
Source code
The model source code can be found in the NESTML models repository here: izhikevich.