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 quasisynchronous 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.