# Command: aeif_cond_beta_multisynapse

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Name:

    aeif_cond_beta_multisynapse - Conductance based adaptive exponential
      integrate-and-fire neuron model according
      to Brette and Gerstner (2005) with
      multiple synaptic rise time and decay
      time constants, and synaptic conductance
      modeled by a beta function.

Examples:

      import nest
      import numpy as np

      neuron = nest.Create('aeif_cond_beta_multisynapse')
      nest.SetStatus(neuron, {"V_peak": 0.0, "a": 4.0, "b":80.5})
      nest.SetStatus(neuron, {'E_rev':[0.0,0.0,0.0,-85.0],
      'tau_decay':[50.0,20.0,20.0,20.0],
      'tau_rise':[10.0,10.0,1.0,1.0]})

      spike = nest.Create('spike_generator', params = {'spike_times':
      np.array([10.0])})

      voltmeter = nest.Create('voltmeter', 1, {'withgid': True})

      delays=[1.0, 300.0, 500.0, 700.0]
      w=[1.0, 1.0, 1.0, 1.0]
      for syn in range(4):
      nest.Connect(spike, neuron, syn_spec={'model': 'static_synapse',
      'receptor_type': 1 + syn,
      'weight': w[syn],
      'delay': delays[syn]})

      nest.Connect(voltmeter, neuron)

      nest.Simulate(1000.0)
      dmm = nest.GetStatus(voltmeter)[0]
      Vms = dmm["events"]["V_m"]
      ts = dmm["events"]["times"]
      import pylab
      pylab.figure(2)
      pylab.plot(ts, Vms)
      pylab.show()

Description:

      aeif_cond_beta_multisynapse is a conductance-based adaptive exponential
      integrate-and-fire neuron model. It allows an arbitrary number of synaptic
      rise time and decay time constants. Synaptic conductance is modeled by a
      beta function, as described by A. Roth and M.C.W. van Rossum
      in Computational Modeling Methods for Neuroscientists, MIT Press 2013,
      Chapter 6.

      The time constants are supplied by two arrays, "tau_rise" and "tau_decay" for
      the synaptic rise time and decay time, respectively. The synaptic
      reversal potentials are supplied by the array "E_rev". The port numbers
      are automatically assigned in the range from 1 to n_receptors.
      During connection, the ports are selected with the property "receptor_type".

      The membrane potential is given by the following differential equation:
      C dV/dt = -g_L(V-E_L) + g_L*Delta_T*exp((V-V_T)/Delta_T) + I_syn_tot(V, t)
     	- w + I_e

      where:
      I_syn_tot(V,t) = \sum_i g_i(t) (V	- E_{rev,i}) ,

      the synapse i is excitatory or inhibitory depending on the value of E_{rev,i}
      and the differential equation for the spike-adaptation current w is:

      tau_w * dw/dt = a(V	- E_L)	- w

      When the neuron fires a spike, the adaptation current w <- w + b.

Parameters:

      C_m	 double	- Capacity of the membrane in pF
      t_ref	 double	- Duration of refractory period in ms.
      V_reset   double	- Reset value for V_m after a spike. In mV.
      E_L	 double	- Leak reversal potential in mV.
      g_L	 double	- Leak conductance in nS.
      I_e	 double	- Constant external input current in pA.
      Delta_T   double	- Slope factor in mV
      V_th	 double	- Spike initiation threshold in mV
      V_peak	 double	- Spike detection threshold in mV.

      Adaptation parameters:
      a	 double	- Subthreshold adaptation in nS.
      b	 double	- Spike-triggered adaptation in pA.
      tau_w	 double	- Adaptation time constant in ms

      Synaptic parameters
      E_rev	 double vector	- Reversal potential in mV.
      tau_rise  double vector	- Rise time of synaptic conductance in ms (beta
      function).
      tau_decay double vector	- Decay time of synaptic conductance in ms (beta
      function).

      Integration parameters
      gsl_error_tol  double	- This parameter controls the admissible error of the
      GSL integrator. Reduce it if NEST complains about
      numerical instabilities.

Require:

    HAVE_GSL

Receives:

    SpikeEvent, CurrentEvent, DataLoggingRequest

      author: Bruno Golosio 07/10/2016

Sends:

    SpikeEvent

SeeAlso:

- aeif_cond_alpha_multisynapse

Source:

    /opt/conda/conda-bld/nest_1524088722951/work/nest-2.14.0/models/aeif_cond_beta_multisynapse.h

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