Bistable kinetic model driven by correlated noises: Unified colored-noise approximation

Abstract

A Fokker-Planck equation for a general one-dimensional non-Markovian system driven by correlated Gaussian noises is derived by means of an extended unified colored-noise approximation. The general stationary probability distribution (SPD) is obtained. The SPD contains three important limits: the uncorrelated noise limit, the white noise limit, and the usual uncorrelated white noise limit. The following important physical aspects have been revealed by virtue of the above-mentioned SPD. (1) In contrast to the well known case of uncorrelated white noises where the parameter of additive noise cannot enter the extremal equation of SPD, now the additive noise parameter does enter the extremal equation as a non-Markovian effect even if the system is driven by uncorrelated noises. (2) When the correlation between the noises does exist, the SPD contains information caused by both correlation and color of the noises. The general results obtained in this Brief Report are applied to a bistable kinetic model. We find for the steady state of the model that in the case of correlated noises, the symmetry of SPD under the reflection of the state variable x with respect to the origin is destroyed. However in the case of non-Markovian processes driven by uncorrelated noises, the above symmetry is preserved.