Warning

This is A PREVIEW for NEST 3.0 and NOT an OFFICIAL RELEASE! Some functionality may not be available and information may be incomplete!

# izhikevich – Izhikevich neuron model¶

## Description¶

Implementation of the simple spiking neuron model introduced by Izhikevich 1. The dynamics are given by:

$dV_m/dt &= 0.04 V_m^2 + 5 V_m + 140 - u + I du/dt &= a (b V_m - u)$
$\begin{split}&\text{if}\;\;\; V_m \geq V_{th}:\\ &\;\;\;\; V_m \text{ is set to } c\\ &\;\;\;\; u \text{ is incremented by } d\\ & \, \\ &v \text{ jumps on each spike arrival by the weight of the spike}\end{split}$

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 $$V_m$$, rather than the previous value

2. the variable $$V_m$$ 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 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

## References¶

1(1,2)

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

SpikeEvent