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.(l) The MFPT of the system is affected by the correlation time T and the correlation strength λ, T and λ play opposing roles in the MFPT. (2) For the case of perfectly correlated noises (λ = l), the MFPT corresponding to α > D and α < D (α and D are the additive noise and multiplicative noise intensities, respectively) exhibit the same behaviors and the MFPT for
α = D is continuous, which is very different from the case of T = 0 Phys. Rev. E 53 (1996) 5764.