gauss_rate – Rate neuron model with Gaussian gain function
==========================================================

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

``gauss_rate`` is an implementation of a nonlinear rate model with input

.. math::

   input(h) = g \cdot \exp( -( x - \mu )^2 / ( 2 \cdot \sigma^2 ) )

It either models a rate neuron with input noise (see ``rate_neuron_ipn``)
or a rate transformer (see ``rate_transformer_node``).
Input transformation can either be applied to individual inputs
or to the sum of all inputs.

The model supports connections to other rate models with either zero or
non-zero delay, and uses the ``secondary_event`` concept introduced with
the gap-junction framework.

Nonlinear rate neurons can be created by typing
``nest.Create("gauss_rate_ipn")``. Nonlinear rate transformers can be
created by typing ``nest.Create("rate_transformer_gauss")``.

See also [1]_, [2]_.

Parameters
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The following parameters can be set in the status dictionary. Note
that some of the parameters only apply to rate neurons and not to rate
transformers.

=================  ======= ==============================================
 rate              real    Rate (unitless)
 tau               ms      Time constant of rate dynamics
 mu                real    Mean input
 sigma             real    Noise parameter
 g                 real    Gain parameter
 mu                real    Mean of the Gaussian gain function
 sigma             real    Standard deviation of Gaussian gain function
 rectify_rate      real    Rectifying rate
 linear_summation  boolean Specifies type of non-linearity (see above)
 rectify_output    boolean Switch to restrict rate to values >= rectify_rate
=================  ======= ==============================================

Note:

The boolean parameter ``linear_summation`` determines whether the
input from different presynaptic neurons is first summed linearly and
then transformed by a nonlinearity (true), or if the input from
individual presynaptic neurons is first nonlinearly transformed and
then summed up (false). Default is true.

References
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.. [1] Hahne J, Dahmen D, Schuecker J, Frommer A, Bolten M, Helias M, Diesmann
       M. (2017). Integration of continuous-time dynamics in a spiking neural
       network simulator. Frontiers in Neuroinformatics, 11:34.
       DOI: https://doi.org/10.3389/fninf.2017.00034

.. [2] Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann Mi
       (2015). A unified framework for spiking and gap-junction interactions
       in distributed neuronal network simulations. Frontiers in
       Neuroinformatics, 9:22. DOI: https://doi.org/10.3389/fninf.2015.00022

Sends
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InstantaneousRateConnectionEvent, DelayedRateConnectionEvent

Receives
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InstantaneousRateConnectionEvent, DelayedRateConnectionEvent,
DataLoggingRequest

See also
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:doc:`Neuron <index_neuron>`, :doc:`Rate <index_rate>`