izhikevich_psc_exp – Izhikevich neuron model with exponential postsynaptic currents
===================================================================================

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

Implementation of the simple spiking neuron model introduced by Izhikevich
[1]_, with postsynaptic currents in the form of truncated exponentials.
The dynamics are given by:

.. math::

  \frac{dV_m}{dt} &= 0.04 V_m^2 + 5 V_m + 140 - u + I \\
  \frac{du}{dt} &= a (b V_m - u)


.. math::

  &\text{if}\;\;\; V_m \geq V_{th}:\\
  &\;\;\;\; V_m \text{ is set to } c\\
  &\;\;\;\; u \text{ is incremented by } d\\
  & \, \\
  &v \text{ jumps on each spike arrival by the weight of the spike}

This implementation uses the standard technique for forward Euler integration.

Parameters
++++++++++

The following parameters can be set in the status dictionary.

======================= =======  ==============================================
 V_m                    mV       Membrane potential
 I_syn                  pA       Synaptic current
 u                      mV       Membrane potential recovery variable
 V_th                   mV       Spike threshold
 a                      real     Describes time scale of recovery variable
 b                      real     Sensitivity of recovery variable
 c                      mV       After-spike reset value of V_m
 d                      mV       After-spike reset value of u
 I_e                    pA       Constant input current
 t_ref                  ms       Refractory time
 tau_syn                ms       Time constant of synaptic current
 den_delay              ms       Dendritic delay
======================= =======  ==============================================

References
++++++++++

.. [1] Izhikevich EM (2003). Simple model of spiking neurons. IEEE Transactions
       on Neural Networks, 14:1569-1572. DOI:
https://doi.org/10.1109/TNN.2003.820440