# lin_rate – Linear rate model¶

## Description¶

lin_rate is an implementation of a rate model with linear input function $$input(h) = g \cdot h$$. 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).

Linear rate neurons support multiplicative coupling which can be switched on and off via the boolean parameter mult_coupling (default=false). In case multiplicative coupling is active, the excitatory input of the model is multiplied with the function $$mult\_coupling\_ex(rate) = g_{ex} \cdot ( \theta_{ex} - rate )$$ and the inhibitory input is multiplied with the function $$mult\_coupling\_in(rate) = g_{in} \cdot ( \theta_{in} + rate )$$.

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

Linear rate neurons can be created by typing nest.Create("lin_rate_ipn") or nest.Create("lin_rate_opn") for input noise or output noise, respectively. Linear rate transformers can be created by typing nest.Create("rate_transformer_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 lambda real Passive decay rate mu real Mean input sigma real Noise parameter g real Gain parameter mult_coupling boolean Switch to enable/disable multiplicative coupling g_ex real Linear factor in multiplicative coupling g_in real Linear factor in multiplicative coupling theta_ex real Shift in multiplicative coupling theta_in real Shift in multiplicative coupling rectify_rate real Rectifying rate 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 Neuroinformatics, 9:22. DOI: https://doi.org/10.3389/fninf.2015.00022

## Sends¶

InstantaneousRateConnectionEvent, DelayedRateConnectionEvent