# izhikevich – Izhikevich neuron model¶

## Description¶

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

As published in 1, the numerics differs from the standard forward Euler technique in two ways:

the new value of \(u\) is calculated based on the new value of \(V_m\), rather than the previous value

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).

For a detailed analysis and discussion of the numerical issues in the original publication, see 2.

## 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

- 2
Pauli R, Weidel P, Kunkel S, Morrison A (2018). Reproducing polychronization: A guide to maximizing the reproducibility of spiking network models. Frontiers in Neuroinformatics, 12. DOI: https://www.frontiersin.org/article/10.3389/fninf.2018.00046

## Sends¶

SpikeEvent

## Receives¶

SpikeEvent, CurrentEvent, DataLoggingRequest