Mean first-passage time of a bistable kinetic model driven by cross-correlated noises

Abstract

The transient properties of a bistable system driven by cross-correlated noises are investigated; the correlation times of the correlations between the noises are nonzero. The mean first-passage time (MFPT) is calculated. From numerical computations we find the following: (1) The MFPT of the system is affected by both the correlation time τ and the correlation strength λ; (2) τ and λ play opposing roles in the MFPT; (3) when λ or $\alpha /D(\alpha$ and D are the additive and multiplicative noise intensities respectively) are far away from 1, the MFPT as a function of τ is monotonic; however, when both $\alpha /D$ and λ approach 1, the MFPT as a function of τ is nonmonotonic; (4) for the case of perfectly correlated noises (λ=1), the MFPT corresponding to $\alpha >D$ and $\alpha <D$ exhibit the same behaviors and the MFPT for $\alpha =D$ is continuous, which is very different from the case of the $\tau =0\mathrm{}$ [Phys. Rev. E 53, 5764 (1996)].