Finite size fluctuations and stochastic resonance in globally coupled bistable systems

TL;DR

This paper investigates how finite-size effects influence stochastic resonance in globally coupled bistable oscillators, using stochastic equations and simplified models to explain large observed gains.

Contribution

It introduces new models based on stochastic calculus and effective potentials to analyze finite-size fluctuations and stochastic resonance in coupled bistable systems.

Findings

Finite size causes significant fluctuations affecting resonance behavior.

Models successfully explain large gains observed in experiments.

Asymptotic approximations are valid for large N.

Abstract

The dynamics of a system formed by a finite number $N$ of globally coupled bistable oscillators and driven by external forces is studied focusing on a global variable defined as the arithmetic mean of each oscillator variable. Several models based on truncation schemes of a hierarchy of stochastic equations for a set of fluctuating cumulant variables are presented. This hierarchy is derived using It\^o stochastic calculus, and the noise terms in it are treated using an asymptotic approximation valid for large $N$. In addition, a simplified one-variable model based on an effective potential is also considered. These models are tested in the framework of the phenomenon of stochastic resonance. In turn, they are used to explain in simple terms the very large gains recently observed in these finite systems.