izhikevich - Izhikevich neuron model
Implementation of the simple spiking neuron model introduced by Izhikevich
[1]. The dynamics are given by:
@f[
dv/dt = 0.04*v^2 + 5*v + 140 - u + I \\
du/dt = a*(b*v - u)] @f]
if \f$ v >= V_{th} \f$:
v is set to c
u is incremented by d
v jumps on each spike arrival by the weight of the spike.
As published in [1], the numerics differs from the standard forward Euler
technique in two ways:
1) the new value of u is calculated based on the new value of v, rather than
the previous value
2) the variable v is updated using a time step half the size of that used to
update variable u.
This model offers both forms of integration, they can be selected using the
boolean parameter consistent_integration. To reproduce some results published
on the basis of this model, it is necessary to use the published form of the
dynamics. In this case, consistent_integration must be set to false. For all
other purposes, it is recommended to use the standard technique for forward
Euler integration. In this case, consistent_integration must be set to true
(default).
The following parameters can be set in the status dictionary.
\verbatim embed:rst
======================= ======= ==============================================
V_m mV Membrane potential
U_m mV Membrane potential recovery variable
V_th mV Spike threshold
I_e pA Constant input current (R=1)
V_min mV Absolute lower value for the membrane potential
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_m
consistent_integration boolean Use standard integration technique
======================= ======= ==============================================
\endverbatim
SpikeEvent, CurrentEvent, DataLoggingRequest
SpikeEvent
\verbatim embed:rst
.. [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
\endverbatim
Hanuschkin, Morrison, Kunkel
2009
/var/www/debian/nest/nest-simulator-2.18.0/models/izhikevich.h