izhikevich - Izhikevich neuron model
Implementation of the simple spiking neuron model introduced by Izhikevich
[1]. The dynamics are given by:
dv/dt = 0.04*v^2 + 5*v + 140 - u + I
du/dt = a*(b*v - u)

if v >= V_th:
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

The following parameters can be set in the status dictionary.

V_m double - Membrane potential in mV
U_m double - Membrane potential recovery variable
V_th double - Spike threshold in mV.
I_e double - Constant input current in pA. (R=1)
V_min double - Absolute lower value for the membrane potential.
a double - describes time scale of recovery variable
b double - sensitivity of recovery variable
c double - after-spike reset value of V_m
d double - after-spike reset value of U_m
consistent_integration bool - use standard integration technique

SpikeEvent, CurrentEvent, DataLoggingRequest  

[1] Izhikevich, Simple Model of Spiking Neurons,
IEEE Transactions on Neural Networks (2003) 14:1569-1572

Hanuschkin, Morrison, Kunkel  
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