Stochastic dynamics of the triple-well potential systems driven by colored noise

TL;DR

This paper extends a stochastic averaging technique to analyze the dynamics of triple-well potential systems driven by colored noise, providing accurate analytical stationary probability densities and exploring noise effects on system behavior.

Contribution

The paper introduces an energy-dependent frequency-based stochastic averaging method tailored for triple-well systems with colored noise, improving accuracy and applicability over traditional methods.

Findings

The proposed method accurately predicts stationary probability densities.

Colored noise significantly influences transition dynamics and symmetry.

Additive noise can induce coherence resonance, unlike multiplicative noise.

Abstract

A stochastic averaging technique based on energy-dependent frequency is extended to dynamical systems with triple-well potential driven by colored noise. The key procedure is the derivation of energy-dependent frequency according to the four different motion patterns in triple-well potential. Combined with the stochastic averaging of energy envelope, the analytical stationary probability density (SPD) of tri-stable systems can be obtained. Two cases of strongly nonlinear triple-well potential systems are presented to explore the effects of colored noise and validate the effectiveness of the proposed method. Results show that the proposed method is well verified by numerical simulations, and has significant advantages, such as high accuracy, small limitation and easy application in multi-stable systems, compared with the traditional stochastic averaging method. Colored noise plays a significant constructive role in modulating transition strength, stochastic fluctuation range and symmetry of triple-well potential. While, the additive and multiplicative colored noises display quite different effects on the features of coherence resonance (CR). Choosing a moderate additive noise intensity can induce CR, but the multiplicative colored noise cannot.