# diffusion_connection – Synapse type for instantaneous rate connections between neurons of type siegert_neuron¶

## Description¶

diffusion_connection is a connector to create instantaneous connections between neurons of type siegert_neuron. The connection type is identical to type rate_connection_instantaneous for instantaneous rate connections except for the two parameters drift_factor and diffusion_factor substituting the parameter weight.

These two factor origin from the mean-field reduction of networks of leaky-integrate-and-fire neurons. In this reduction the input to the neurons is characterized by its mean and its variance. The mean is obtained by a sum over presynaptic activities (e.g as in eq.28 in 1), where each term of the sum consists of the presynaptic activity multiplied with the drift_factor. Similarly, the variance is obtained by a sum over presynaptic activities (e.g as in eq.29 in 1), where each term of the sum consists of the presynaptic activity multiplied with the diffusion_factor. Note that in general the drift and diffusion factors might differ from the ones given in eq. 28 and 29., for example in case of a reduction on the single neuron level or in case of distributed in-degrees (see discussion in chapter 5.2 of 1)

The values of the parameters delay and weight are ignored for connections of this type.

## Transmits¶

DiffusionConnectionEvent

## References¶

- 1(1,2,3)
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