# Command: iaf_psc_delta_canon

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Name:

    iaf_psc_delta_canon - Leaky integrate-and-fire neuron model.

Description:

      iaf_psc_delta_canon is an implementation of a leaky integrate-and-fire model
      where the potential jumps on each spike arrival.

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

      Spikes arriving while the neuron is refractory, are discarded by
      default. If the property "refractory_input" is set to true, such
      spikes are added to the membrane potential at the end of the
      refractory period, dampened according to the interval between
      arrival and end of refractoriness.

      The linear subthresold dynamics is integrated by the Exact
      Integration scheme [1]. The neuron dynamics are solved exactly in
      time. Incoming and outgoing spike times are handled precisely [3].

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

      Spikes can occur either on receipt of an excitatory input spike, or
      be caused by a depolarizing input current.  Spikes evoked by
      incoming spikes, will occur precisely at the time of spike arrival,
      since incoming spikes are modeled as instantaneous potential
      jumps. Times of spikes caused by current input are determined
      exactly by solving the membrane potential equation. Note that, in
      contrast to the neuron models discussed in [3,4], this model has so
      simple dynamics that no interpolation or iterative spike location
      technique is required at all.

      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_delta_canon 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	- Capacitance 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.
      I_e	 double	- Constant input current in pA.
      V_min	 double	- Absolute lower value for the membrane potential in mV.

      refractory_input bool	- If true, do not discard input during
      refractory period. Default: false.

Receives:

    SpikeEvent, CurrentEvent, DataLoggingRequest

      Author:  May 2006, Plesser; based on work by Diesmann, Gewaltig, Morrison,
      Straube, Eppler

Sends:

    SpikeEvent

Remarks:

      The iaf_psc_delta_canon neuron accepts CurrentEvent connections.
      However, the present method for transmitting CurrentEvents in
      NEST (sending the current to be applied) is not compatible with off-grid
      currents, if more than one CurrentEvent-connection exists. Once CurrentEvents
      are changed to transmit change-of-current-strength, this problem will
      disappear and the canonical neuron will also be able to handle CurrentEvents.

      The present implementation uses individual variables for the
      components of the state vector and the non-zero matrix elements of
      the propagator.  Because the propagator is a lower triangular matrix
      no full matrix multiplication needs to be carried out and the
      computation can be done "in place" i.e. no temporary state vector
      object is required.

      The template support of recent C++ compilers enables a more succinct
      formulation without loss of runtime performance already at minimal
      optimization levels. A future version of iaf_psc_delta_canon will probably
      address the problem of efficient usage of appropriate vector and
      matrix objects.

      Please note that this node is capable of sending precise spike times
      to target nodes (on-grid spike time plus offset). If this node is
      connected to a spike_detector, the property "precise_times" of the
      spike_detector has to be set to true in order to record the offsets
      in addition to the on-grid spike times.

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. To appear in Neural Computation.
      [4] 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

SeeAlso:

- iaf_psc_delta
- iaf_psc_exp_ps

Source:

    /opt/conda/conda-bld/nest_1510212701067/work/nest-2.14.0/precise/iaf_psc_delta_canon.h

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