jonke_synapse – Synapse type for spike-timing dependent plasticity with additional additive factors.
====================================================================================================

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

jonke_synapse is a connector to create synapses with spike time
dependent plasticity. Unlike ``stdp_synapse``, we use the update equations:

.. math::

   \Delta w &= \lambda \cdot w_{max} \cdot (K_+(w) \cdot F_+(t) - \beta)  & \quad  if t - t_j^(k) > 0 \\
   \Delta w &= \lambda \cdot w_{max} \cdot (-alpha \cdot K_-(w) \cdot F_-(t) - \beta)  & \quad  else

where

.. math::

   K_+(w) &= \exp(\nu_+ w) \\
   K_-(w) &= \exp(\nu_- w)

and

.. math::

   F_+(t) &= \exp((t - t_j^(k))/\tau_+) \\
   F_-(t) &= \exp((t - t_j^(k))/\tau_-)

This makes it possible to implement update rules which approximate the
rule stated in [1]_, and for examples, the rules given in [2]_ and [3]_.

.. warning::

   This synaptic plasticity rule does not take
   :ref:`precise spike timing <sim_precise_spike_times>` into
   account. When calculating the weight update, the precise spike time part
   of the timestamp is ignored.

Parameters
++++++++++

========== ========  ======================================================
 lambda     double    Step size
 Wmax       double    Maximum allowed weight, note that this scales each
                      weight update
 alpha      double    Determine shape of depression term
 mu_plus    double    Set weight dependency of facilitating update
 mu_minus   double    Set weight dependency of depressing update
 tau_plus   double    Time constant of STDP window, potentiation in ms
 beta       double    Set negative offset for both updates
========== ========  ======================================================

(tau_minus is defined in the postsynaptic neuron.)

Transmits
+++++++++

SpikeEvent

References
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.. [1] Nessler, Bernhard, et al. "Bayesian computation emerges in generic
       cortical microcircuits through spike-timing-dependent plasticity." PLoS
       computational biology 9.4 (2013): e1003037.
.. [2] Legenstein, Robert, et al. "Assembly pointers for variable binding in
       networks of spiking neurons." arXiv preprint arXiv:1611.03698 (2016).
.. [3] Jonke, Zeno, et al. "Feedback inhibition shapes emergent computational
       properties of cortical microcircuit motifs." arXiv preprint
       arXiv:1705.07614 (2017).

See also
++++++++
:doc:`Synapse <index_synapse>`, :doc:`Spike-Timing-Dependent Plasticity <index_spike-timing-dependent plasticity>`