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

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.