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We study the fluctuation-activated transition process in a system of twocoupled bistable oscillators, in which each oscillator is driven by oneconstant force and an independent Gaussian white noise. The transition pathwayhas been identified and the transition rate has been computed as the couplingstrength $\mu$ and the mismatch $\sigma$ in the force constants are varied. Foridentical oscillators ($\sigma=0$), the transition undergoes a change from atwo-step process with two candidate pathways to a one-step process with alsotwo candidate pathways to a one-step process with a single pathway as $\mu$ isincreased. For nonidentical oscillators ($\sigma\neq0$), a novel transitionemerges that is a mixture of a two-step pathway and a one-step pathway.Interestingly, we find that the total transition rate depends nonmonotonicallyon $\mu$: a maximal rate appears in an intermediate magnitude of $\mu$.Moreover, in the presence of weak coupling the rate also exhibits an unexpectedmaximum as a function of $\sigma$. The results are in an excellent agreementwith our numerical simulations by forward flux sampling.

Complex activated transition in a system of two coupled bistable oscillators