ht_synapse – Synapse with depression after Hill & Tononi (2005)
===============================================================

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

This synapse implements the depression model described in [1]_, p 1678.

Synaptic dynamics are given by

.. math::

    \frac{dP(t)}{dt} &= \frac{1}{\tau_\mathrm{P}} \left( 1 - P \right)  \\
    P(t=0) &= 1 \\

Upon the arrival of a presynaptic spike at time :math:`t_\mathrm{sp}`, the value of :math:`P` is updated as follows:

.. math::

    P \leftarrow (1 - \delta_\mathrm{P}) P

:math:`w(t) = w_\mathrm{max} \cdot P(t)` is the resulting synaptic weight.

For implementation details see:
`HillTononi_model <../model_details/HillTononiModels.ipynb>`_

.. 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
++++++++++

The following parameters can be set in the status dictionary:

========  ======  =========================================================
 tau_P    ms      Synaptic vesicle pool recovery time constant
 delta_P  real    Fractional change in vesicle pool on incoming spikes
                  (unitless)
 P        real    Current size of the vesicle pool (unitless, 0 <= P <= 1)
========  ======  =========================================================

References
++++++++++

.. [1] Hill S, Tononi G (2005). Modeling sleep and wakefulness in the
       thalamocortical system. Journal of Neurophysiology. 93:1671-1698.
       DOI: https://doi.org/10.1152/jn.00915.2004

Transmits
+++++++++

SpikeEvent

See also
++++++++

ht_neuron, tsodyks_synapse, stdp_synapse, static_synapse

Examples using this model
+++++++++++++++++++++++++

.. listexamples:: ht_synapse