Complex activated transition in a system of two coupled bistable oscillators

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.