# Command: amat2_psc_exp

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Name:

    amat2_psc_exp - Non-resetting leaky integrate-and-fire neuron model
      with exponential PSCs and adaptive threshold.

Description:

      amat2_psc_exp is an implementation of a leaky integrate-and-fire model
      with exponential shaped postsynaptic currents (PSCs). Thus, postsynaptic
      currents have an infinitely short rise time.

      The threshold is lifted when the neuron is fired and then decreases in a
      fixed time scale toward a fixed level [3].

      The threshold crossing is followed by a total refractory period
      during which the neuron is not allowed to fire, even if the membrane
      potential exceeds the threshold. The membrane potential is NOT reset,
      but continuously integrated.

      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].

Parameters:

      The following parameters can be set in the status dictionary:

      C_m	 double	- Capacity of the membrane in pF
      E_L	 double	- Resting potential in mV
      tau_m	 double	- Membrane time constant in ms
      tau_syn_ex   double	- Time constant of postsynaptic excitatory currents in ms
      tau_syn_in   double	- Time constant of postsynaptic inhibitory currents in ms
      t_ref	 double	- Duration of absolute refractory period (no spiking) in
      ms
      V_m	 double	- Membrane potential in mV
      I_e	 double	- Constant input current in pA
      t_spike	 double	- Point in time of last spike in ms
      tau_1	 double	- Short time constant of adaptive threshold in ms
      [3, eqs 2-3]
      tau_2	 double	- Long time constant of adaptive threshold in ms
      [3, eqs 2-3]
      alpha_1	 double	- Amplitude of short time threshold adaption in mV
      [3, eqs 2-3]
      alpha_2	 double	- Amplitude of long time threshold adaption in mV
      [3, eqs 2-3]
      tau_v	 double	- Time constant of kernel for voltage-dependent threshold
      component in ms [3, eqs 16-17]
      beta	 double	- Scaling coefficient for voltage-dependent threshold
      component in 1/ms [3, eqs 16-17]
      omega	 double	- Resting spike threshold in mV (absolute value, not
      relative to E_L as in [3])

      The following state variables can be read out with the multimeter device:

      V_m	 Non-resetting membrane potential
      V_th	 Two-timescale adaptive threshold

Receives:

    SpikeEvent, CurrentEvent, DataLoggingRequest

Sends:

    SpikeEvent

Remarks:

      tau_m != tau_syn_{ex,in} is required by the current implementation to avoid a
      degenerate case of the ODE describing the model [1]. For very similar values,
      numerics will be unstable.

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] Kobayashi R, Tsubo Y and Shinomoto S (2009) Made-to-order
      spiking neuron model equipped with a multi-timescale adaptive
      threshold. Front. Comput. Neurosci. 3:9. doi:10.3389/neuro.10.009.2009
      [4] Yamauchi S, Kim H and Shinomoto S (2011) Elemental spiking neuron model
      for reproducing diverse firing patterns and predicting precise
      firing times. Front. Comput. Neurosci. 5:42.
      doi: 10.3389/fncom.2011.00042

Author:

    Thomas Heiberg & Hans E. Plesser (modified mat2_psc_exp model of
      Thomas Pfeil)

FirstVersion:

    April 2013

Source:

    /opt/conda/conda-bld/nest_1510213973486/work/nest-2.14.0/models/amat2_psc_exp.h

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