**Name:**

izhikevich - Izhikevich neuron model

**Description:**

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

(default).

**Parameters:**

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

**Receives:**

SpikeEvent, CurrentEvent, DataLoggingRequest

**Sends:**

SpikeEvent

**References:**

[1] Izhikevich, Simple Model of Spiking Neurons,

IEEE Transactions on Neural Networks (2003) 14:1569-1572

**Author:**

Hanuschkin, Morrison, Kunkel

**FirstVersion:**

2009

**SeeAlso:**

**Source:**

/home/graber/work-nest/nest-git/nest-simulator/models/izhikevich.h