Effects of multiplicative noises on synchronization in finite $N$-unit stochastic ensembles: Augmented moment approach

Abstract

We have studied the synchronization in finite $N$-unit FitzHugh-Nagumo neuron ensembles subjected to additive and multiplicative noises, by using the augmented moment method (AMM) which is reformulated with the use of the Fokker-Planck equation. It has been shown that for diffusive couplings, the synchronization may be enhanced by multiplicative noises while additive noises are detrimental to the synchronization. In contrast, for sigmoid coupling, both additive and multiplicative noises deteriorate the synchronization. The synchronization depends not only on the type of noises but also on the kind of couplings.