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 |