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 ͑MFPT͒ is calculated. From numerical computations we find the following: ͑1͒ The MFPT of the system is affected by both the correlation time and the correlation strength ; ͑2͒ and play opposing roles in the MFPT; ͑3͒ when or ␣/D(␣ and D are the additive and multiplicative noise intensities respectively͒ are far away from 1, the MFPT as a function of is monotonic; however, when both ␣/D and approach 1, the MFPT as a function of is nonmonotonic; ͑4͒ for the case of perfectly correlated noises ͑ϭ1͒, the MFPT corresponding to ␣ϾD and ␣ϽD exhibit the same behaviors and the MFPT for ␣ϭD is continuous, which is very different from the case of the ϭ0 ͓Phys. Rev. E 53, 5764 ͑1996͔͒. ͓S1063-651X͑99͒14203-X͔ PACS number͑s͒: 05.40.Ca

An open-loop approach to calculate noise-induced transitions

“…5b). This is not fully surprising because it has been known that additional factors like non-zero cross-correlations between the fluctuations have to be taken into account in the presence of nonlinear reactions A large number of studies have explored the effect of cross-correlation on the transitions (Fuliński and Telejko, 1991;Mei et al, 1999).…”

Mean First-Passage Time in a Bistable Kinetic Model with Stochastic Potentials

“…In recent years several papers have dealt with the derivation of exact expressions for the MFPT of the bistable system (Behn et al, 1993;Jia and Li, 1996;Kus and Wodkiewicz, 1993;Laio et al, 2001;Mei et al, 1999;Porra and Lindenberg, 1995;Venkatesh and Patnaik, 1993). Behn and his co-workers (Behn et al, 1993)studied the MFPT of the system driven by a superposition of suitably scaled independent dichotomous Markovian processes with natural boundary condition.…”

Kramers problem for a dimer: Effect of noise correlations

“…However, all these studies have focused on uncorrelated noise processes, whereas it is known that noises from identical origin are generally correlated [9]. Such correlations significantly affect the dynamics of a particle in a bistable potential [10][11][12][13], and are known to induce nonzero transport in periodic potentials due to symmetry breaking [14]. The observations motivate us to study the effect of noise correlations on the dynamics of extended objects.…”