Transient properties of a bistable system driven by cross-correlated noises: Correlation times are nonzero case

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 explicit expression of the mean first-passage time (MFPT) is obtained. From numerical computations we find the following.(1) The MPPT of the system is affected by the correlation time tau and the correlation strength lambda, tau and lambda play opposing roles in the MFPT. (2) For the case of perfectly correlated noises (lambda = 1), the MFPT corresponding to alpha > D and alpha < D (alpha and D are the additive noise and multiplicative noise intensities, respectively) exhibit the same behaviors and the MFPT for alpha = D is continuous, which is very different from the case of tau = 0 [Phys. Rev. E 53 (1996) 5764].