sigmoid_rate – Rate neuron model with sigmoidal gain function
=============================================================

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

``sigmoid_rate`` is an implementation of a nonlinear rate model with input
function :math:`input(h) = g / ( 1. + \exp( -\beta \cdot ( h - \theta ) ) )`.

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.

The following parameters can be set in the status dictionary.

Nonlinear rate neurons can be created by typing
``nest.Create('sigmoid_rate_ipn')``. Nonlinear rate transformers can be
created by typing ``nest.Create('rate_transformer_sigmoid')``.

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

Parameters
++++++++++

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
 beta               real    Slope parameter
 theta              real    Threshold
 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
++++++++++

.. [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 M
       (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
+++++

InstantaneousRateConnectionEvent, DelayedRateConnectionEvent

Receives
++++++++

InstantaneousRateConnectionEvent, DelayedRateConnectionEvent,
DataLoggingRequest

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