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This is A PREVIEW for NEST 3.0 and NOT an OFFICIAL RELEASE! Some functionality may not be available and information may be incomplete!

# threshold_lin_rate – Rate model with threshold-linear gain function¶

## Description¶

threshold_lin_rate is an implementation of a nonlinear rate model with input function $$input(h) = min( max( g * ( h - \theta ), 0 ), \alpha )$$. It either models a rate neuron with input noise (see rate_neuron_ipn), a rate neuron with output noise (see rate_neuron_opn) 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 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.

Nonlinear rate neuron instances can be obtained by creating models of type threshold_lin_rate_ipn for input noise or of type threshold_lin_rate_opn output noise. Nonlinear rate transformers can be obtained by creating models of type rate_transformer_threshold_lin.

## 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 alpha real Second Threshold 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

## 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