# sigmoid_rate – Rate neuron model with sigmoidal gain function¶

## Description¶

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

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’).

## 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