iaf_cond_exp_sfa_rr_neuron
##########################

iaf_cond_exp_sfa_rr - Conductance based leaky integrate-and-fire model with spike-frequency adaptation and relative refractory mechanisms


Description
+++++++++++

iaf_cond_exp_sfa_rr is an implementation of a spiking neuron using integrate-and-fire dynamics with conductance-based
synapses, with additional spike-frequency adaptation and relative refractory mechanisms as described in [2]_, page 166.

Incoming spike events induce a post-synaptic change of conductance modelled by an exponential function. The exponential
function is normalised such that an event of weight 1.0 results in a peak current of 1 nS.

Outgoing spike events induce a change of the adaptation and relative refractory conductances by q_sfa and q_rr,
respectively. Otherwise these conductances decay exponentially with time constants tau_sfa and tau_rr, respectively.

References
++++++++++

.. [1] Meffin H, Burkitt AN, Grayden DB (2004). An analytical
       model for the large, fluctuating synaptic conductance state typical of
       neocortical neurons in vivo. Journal of Computational Neuroscience,
       16:159-175.
       DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81
.. [2] Dayan P, Abbott LF (2001). Theoretical neuroscience: Computational and
       mathematical modeling of neural systems. Cambridge, MA: MIT Press.
       https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_3006127

See also
++++++++

aeif_cond_alpha, aeif_cond_exp, iaf_chxk_2008

Copyright statement
+++++++++++++++++++

This file is part of NEST.

Copyright (C) 2004 The NEST Initiative

NEST is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 2 of the License, or
(at your option) any later version.

NEST is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with NEST.  If not, see <http://www.gnu.org/licenses/>.


Parameters
++++++++++
.. csv-table::
    :header: "Name", "Physical unit", "Default value", "Description"
    :widths: auto

    
    "V_th", "mV", "-57.0mV", "Threshold potential"    
    "V_reset", "mV", "-70.0mV", "Reset potential"    
    "refr_T", "ms", "0.5ms", "Duration of refractory period"    
    "g_L", "nS", "28.95nS", "Leak conductance"    
    "C_m", "pF", "289.5pF", "Membrane capacitance"    
    "E_exc", "mV", "0mV", "Excitatory reversal potential"    
    "E_inh", "mV", "-75.0mV", "Inhibitory reversal potential"    
    "E_L", "mV", "-70.0mV", "Leak reversal potential (a.k.a. resting potential)"    
    "tau_syn_exc", "ms", "1.5ms", "Synaptic time constant of excitatory synapse"    
    "tau_syn_inh", "ms", "10.0ms", "Synaptic time constant of inhibitory synapse"    
    "q_sfa", "nS", "14.48nS", "Outgoing spike activated quantal spike-frequency adaptation conductance increase"    
    "q_rr", "nS", "3214.0nS", "Outgoing spike activated quantal relative refractory conductance increase"    
    "tau_sfa", "ms", "110.0ms", "Time constant of spike-frequency adaptation"    
    "tau_rr", "ms", "1.97ms", "Time constant of the relative refractory mechanism"    
    "E_sfa", "mV", "-70.0mV", "spike-frequency adaptation conductance reversal potential"    
    "E_rr", "mV", "-70.0mV", "relative refractory mechanism conductance reversal potential"    
    "I_e", "pA", "0pA", "constant external input current"



State variables
+++++++++++++++

.. csv-table::
    :header: "Name", "Physical unit", "Default value", "Description"
    :widths: auto

    
    "V_m", "mV", "E_L", "Membrane potential"    
    "refr_t", "ms", "0ms", "Refractory period timer"    
    "g_sfa", "nS", "0nS", "inputs from the sfa conductance"    
    "g_rr", "nS", "0nS", "inputs from the rr conductance"




Equations
+++++++++



.. math::
   \frac{ dg_{sfa} } { dt }= \frac{ -g_{sfa} } { \tau_{sfa} }

.. math::
   \frac{ dg_{rr} } { dt }= \frac{ -g_{rr} } { \tau_{rr} }

.. math::
   \frac{ dV_{m} } { dt }= \frac 1 { C_{m} } \left( { (-I_{L} + I_{e} + I_{stim} - I_{syn,exc} - I_{syn,inh} - I_{sfa} - I_{rr}) } \right) 

.. math::
   \frac{ drefr_{t} } { dt }= \frac{ -1000.0 \cdot \mathrm{ms} } { \mathrm{s} }



Source code
+++++++++++

The model source code can be found in the NESTML models repository here: `iaf_cond_exp_sfa_rr_neuron <https://github.com/nest/nestml/tree/main/models/neurons/iaf_cond_exp_sfa_rr_neuron.nestml>`_.

.. include:: iaf_cond_exp_sfa_rr_neuron_characterisation.rst


.. footer::

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