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

TL;DR

This paper investigates how additive and multiplicative noises affect synchronization in finite FitzHugh-Nagumo neuron ensembles, revealing that noise effects depend on the type of coupling and noise.

Contribution

It introduces an augmented moment method based on the Fokker-Planck equation to analyze noise effects on neural synchronization.

Findings

Multiplicative noise can enhance synchronization with diffusive coupling.

Additive noise generally deteriorates synchronization.

Effects vary with coupling type and noise nature.

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.