# Command: iaf_psc_alpha

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Name:

    iaf_psc_alpha - Leaky integrate-and-fire neuron model.

Description:

      iaf_psc_alpha is an implementation of a leaky integrate-and-fire model
      with alpha-function shaped synaptic currents. Thus, synaptic currents
      and the resulting post-synaptic potentials have a finite rise time.

      The threshold crossing is followed by an absolute refractory period
      during which the membrane potential is clamped to the resting potential.

      The linear subthresold dynamics is integrated by the Exact
      Integration scheme [1]. The neuron dynamics is solved on the time
      grid given by the computation step size. Incoming as well as emitted
      spikes are forced to that grid.

      An additional state variable and the corresponding differential
      equation represents a piecewise constant external current.

      The general framework for the consistent formulation of systems with
      neuron like dynamics interacting by point events is described in
      [1].  A flow chart can be found in [2].

      Critical tests for the formulation of the neuron model are the
      comparisons of simulation results for different computation step
      sizes. sli/testsuite/nest contains a number of such tests.

      The iaf_psc_alpha is the standard model used to check the consistency
      of the nest simulation kernel because it is at the same time complex
      enough to exhibit non-trivial dynamics and simple enough compute
      relevant measures analytically.

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.
      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_ex double	- Rise time of the excitatory synaptic alpha function in ms.
      tau_syn_in double	- Rise time of the inhibitory synaptic alpha function in ms.
      I_e	 double	- Constant external input current in pA.
      V_min	 double	- Absolute lower value for the membrane potential.

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] Rotter S & Diesmann M (1999) Exact simulation of time-invariant linear
      systems with applications to neuronal modeling. Biologial Cybernetics
      81:381-402.
      [2] Diesmann M, Gewaltig M-O, Rotter S, & Aertsen A (2001) State space
      analysis of synchronous spiking in cortical neural networks.
      Neurocomputing 38-40:565-571.
      [3] Morrison A, Straube S, Plesser H E, & Diesmann M (2006) Exact subthreshold
      integration with continuous spike times in discrete time neural network
      simulations. Neural Computation, in press

FirstVersion:

    September 1999
      Author:  Diesmann, Gewaltig

SeeAlso:

- iaf_psc_delta
- iaf_psc_exp
- iaf_cond_exp

Source:

    /opt/conda/conda-bld/nest_1512418773968/work/nest-2.14.0/models/iaf_psc_alpha.h

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