Unified signal response for stochastic resonance in bistable systems

TL;DR

This paper develops a unified theoretical framework describing how noise characteristics, damping, and coupling influence stochastic resonance in bistable systems, providing a comprehensive understanding of signal amplification mechanisms.

Contribution

It introduces a universal response-noise formula applicable to various bistable systems, integrating factors like noise color, damping, and coupling effects.

Findings

Signal response formulas reduce to a Lorentzian form.

Noise color and coupling significantly affect stochastic resonance.

Theoretical explanation of frequency and noise influence on signal amplification.

Abstract

The phenomenon of stochastic resonance, wherein the stimulus-response of a system can be maximized by an intermediate level of noise, has been extensively investigated through linear response theory. As yet a unified response-noise or response-frequency formula embracing diverse factors, such as noise color, damping coefficients, and coupling, is still lacking. In the present work, we theoretically investigate the benefit roles of Gaussian white noise and Ornstein- Uhlenbeck noise on the signal amplification of systems ranging from a single overdamped bistable particle to the mean-field coupled underdamped Duffing oscillators and severally deduce their signal response expressions. We find that the formulas of signal response in these different cases can be reduced to a uniform Lorentz function form. Furthermore, based on the general expression, we explain explicitly the role of driving frequency, coupling and the noise color on stochastic resonance. Our results contribute to a deep theoretical understanding of stochastic resonance in bistable systems.