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 \ensuremath{\tau} and the correlation strength \ensuremath{\lambda}; (2) \ensuremath{\tau} and \ensuremath{\lambda} play opposing roles in the MFPT; (3) when \ensuremath{\lambda} or $\ensuremath{\alpha}/D(\ensuremath{\alpha}$ and D are the additive and multiplicative noise intensities respectively) are far away from 1, the MFPT as a function of \ensuremath{\tau} is monotonic; however, when both $\ensuremath{\alpha}/D$ and \ensuremath{\lambda} approach 1, the MFPT as a function of \ensuremath{\tau} is nonmonotonic; (4) for the case of perfectly correlated noises (\ensuremath{\lambda}=1), the MFPT corresponding to $\ensuremath{\alpha}>D$ and $\ensuremath{\alpha}<D$ exhibit the same behaviors and the MFPT for $\ensuremath{\alpha}=D$ is continuous, which is very different from the case of the $\ensuremath{\tau}=0$ [Phys. Rev. E 53, 5764 (1996)].