# Command: izhikevich

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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:

- iaf_psc_delta
- mat2_psc_exp

Source:

    /opt/conda/conda-bld/nest_1512421404550/work/nest-2.12.0/models/izhikevich.h

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