Mean First-Passage Time of an Asymmetric Kinetic Model Driven by Two Different Kinds of Colored Noises

Abstract

The mean first-passage time (MFPT) of an asymmetric bistable system between multiplicative non-Gaussian noise and additive Gaussian white noise with nonzero cross-correlation time is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker–Planck equation is obtained by applying the unified colored noise approximation and the Novikov Theorem. The steady-state probability distribution (SPD) is also obtained. The basal functional analysis and simplification are employed to obtain the approximate expressions of MFPT T±. The effects of the asymmetry parameter β, the non-Gaussian parameter (measures deviation from Gaussian character) r, the noise correlation times τ and τ2, the coupling coefficient λ, the intensities D and α of noise on the MFPT are discussed. It is found that the asymmetry parameter β, the non-Gaussian parameter r and the coupling coefficient λ can induce phase transition. Moreover, the main findings are that the effect of self-existent parameters (D, α, and τ) of noise and cross-correlation parameters (λ,τ2) between noises on MFPT T± is different.