# Command: iaf_psc_alpha_canon

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Name:

    iaf_psc_alpha_canon - Leaky integrate-and-fire neuron
      with alpha-shape postsynaptic currents; canoncial implementation.

Description:

      iaf_psc_alpha_canon is the "canonical" implementatoin of the leaky
      integrate-and-fire model neuron with alpha-shaped postsynaptic
      currents in the sense of [1].  This is the most exact implementation
      available.

      PSCs are normalized to an amplitude of 1pA.

      The canonical implementation handles neuronal dynamics in a locally
      event-based manner with in coarse time grid defined by the minimum
      delay in the network, see [1]. Incoming spikes are applied at the
      precise moment of their arrival, while the precise time of outgoing
      spikes is determined by interpolation once a threshold crossing has
      been detected. Return from refractoriness occurs precisly at spike
      time plus refractory period.

      This implementation is more complex than the plain iaf_psc_alpha
      neuron, but achieves much higher precision. In particular, it does not
      suffer any binning of spike times to grid points. Depending on your
      application, the canonical application may provide superior overall
      performance given an accuracy goal; see [1] for details.  Subthreshold
      dynamics are integrated using exact integration between events [2].

Parameters:

      The following parameters can be set in the status dictionary.

      V_m	 double	- Membrane potential in mV
      E_L	 double	- Resting membrane potential in mV.
      V_min	 double	- Absolute lower value for the membrane potential.
      C_m	 double	- Capacity of the membrane in pF
      tau_m	 double	- Membrane time constant in ms.
      t_ref	 double	- Duration of refractory period in ms.
      V_th	 double	- Spike threshold in mV.
      V_reset	 double	- Reset potential of the membrane in mV.
      tau_syn	 double	- Rise time of the synaptic alpha function in ms.
      I_e	 double	- Constant external input current in pA.
      Interpol_Order  int	- Interpolation order for spike time:
      0-none, 1-linear, 2-quadratic, 3-cubic

Receives:

    SpikeEvent, CurrentEvent, DataLoggingRequest

Sends:

    SpikeEvent

Remarks:

      If tau_m is very close to tau_syn_ex or tau_syn_in, the model
      will numerically behave as if tau_m is equal to tau_syn_ex or
      tau_syn_in, respectively, to avoid numerical instabilities.
      For details, please see IAF_Neruons_Singularity.ipynb in
      the NEST source code (docs/model_details).

References:

      [1] Morrison A, Straube S, Plesser H E, & Diesmann M (2006) Exact Subthreshold
      Integration with Continuous Spike Times in Discrete Time Neural Network
      Simulations. To appear in Neural Computation.
      [2] Rotter S & Diesmann M (1999) Exact simulation of time-invariant linear
      systems with applications to neuronal modeling. Biologial Cybernetics
      81:381-402.
      [3] Hanuschkin A, Kunkel S, Helias M, Morrison A & Diesmann M (2010)
      A general and efficient method for incorporating exact spike times in
      globally time-driven simulations Front Neuroinformatics, 4:113

Author:

    Diesmann, Eppler, Morrison, Plesser, Straube

SeeAlso:

- iaf_psc_alpha
- iaf_psc_alpha_presc
- iaf_psc_exp_ps

Source:

    /opt/conda/conda-bld/nest_1524088722951/work/nest-2.14.0/precise/iaf_psc_alpha_canon.h

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