Random Networks of Spiking Neurons: Instability in the Xenopus tadpole moto-neural pattern

Abstract

A large network of integrate-and-fire neurons is studied analytically when the synaptic weights are independently randomly distributed according to a Gaussian distribution with arbitrary mean and variance. The relevant order parameters are identified, and it is shown that such network is statistically equivalent to an ensemble of independent integrate-and-fire neurons with each input signal given by the sum of a self-interaction deterministic term and a Gaussian colored noise. The model is able to reproduce the quasi-synchronous oscillations, and the dropout of their frequency, of the central nervous system neurons of the swimming Xenopus tadpole. Predictions from the model are proposed for future experiments.

4 pages, 2 figures (eps), revtex4-2. Post-peer-review author's version. Note: The function P(w) in the integral of Eq. 5 does not appear in the PRL published version because of a typographical omission (courtesy of the author) in a late change of notation. Slightly revised version of the original submission to Physical Review Letters