Optimizing and reducing stochastic resonance by noise color in globally coupled bistable systems

TL;DR

This paper explores how the color of noise affects stochastic resonance in coupled bistable systems, revealing contrasting effects in overdamped and underdamped models through theoretical and numerical analysis.

Contribution

It provides a theoretical and numerical analysis of how noise color influences stochastic resonance differently in overdamped and underdamped bistable systems.

Findings

Noise color weakens stochastic resonance in overdamped systems

Noise color nonmonotonically enhances stochastic resonance in underdamped systems

Theoretical results are verified by numerical integration

Abstract

We investigate the collective signal response of two typical nonlinear dynamical models, the mean-field coupled overdamped bistable oscillators and the underdamped Duffing oscillators, with respect to both the additive Ornstein-Uhlenbeck noise and the weak periodical stimulus. Based on the linear response theory, we theoretically derive the dependences of the ensemble signal response on the noise intensity and driving frequency of both systems. Furthermore, we theoretically demonstrate that the noise color monotonically weakens the strength of stochastic resonance in the overdamped situation, but nonmonotonically strengthens it in the underdamped counterpart. Such a result goes against the conventional wisdom that the color of the additive noise impairs the magnitude of stochastic resonance. Finally, we perform the numerical integration to verify our theoretical results and discuss potential connections with the functional significance of 1/f noise.