Complex activated transition in a system of two coupled bistable oscillators

TL;DR

This paper investigates how coupling strength and force mismatch influence fluctuation-activated transitions in two coupled bistable oscillators, revealing complex pathway changes and nonmonotonic transition rates.

Contribution

It introduces a detailed analysis of transition pathways and rates in coupled oscillators, including the effects of coupling and mismatch, supported by numerical simulations.

Findings

Transition pathway changes from two-step to one-step with increasing coupling

Emergence of a mixed transition pathway for nonidentical oscillators

Transition rate exhibits nonmonotonic dependence on coupling and mismatch

Abstract

We study the fluctuation-activated transition process in a system of two coupled bistable oscillators, in which each oscillator is driven by one constant force and an independent Gaussian white noise. The transition pathway has been identified and the transition rate has been computed as the coupling strength $\mu$ and the mismatch $\sigma$ in the force constants are varied. For identical oscillators ($\sigma=0$), the transition undergoes a change from a two-step process with two candidate pathways to a one-step process with also two candidate pathways to a one-step process with a single pathway as $\mu$ is increased. For nonidentical oscillators ($\sigma\neq0$), a novel transition emerges that is a mixture of a two-step pathway and a one-step pathway. Interestingly, we find that the total transition rate depends nonmonotonically on $\mu$: a maximal rate appears in an intermediate magnitude of $\mu$. Moreover, in the presence of weak coupling the rate also exhibits an unexpected maximum as a function of $\sigma$. The results are in an excellent agreement with our numerical simulations by forward flux sampling.