BISTABLE KINETIC-MODEL DRIVEN BY CORRELATED NOISES - UNIFIED COLORED-NOISE APPROXIMATION

A Fokker-Planck equation for a general one-dimensional non-Markovian s ystem driven by correlated Gaussian noises is derived by means of an e xtended unified colored-noise approximation. The general stationary pr obability distribution (SPD) is obtained. The SPD contains three impor tant limits: the uncorrelated noise limit, the white noise limit, and the usual uncorrelated white noise limit. The following important phys ical aspects have been revealed by virtue of the above-mentioned SPD. (1) In contrast to the well known case of uncorrelated white noises wh ere the parameter of additive noise cannot enter the extremal equation of SPD, now the additive noise parameter does enter the extremal equa tion as a non-Markovian effect even if the system is driven by uncorre lated noises. (2) When the correlation between the noises does exist, the SPD contains information caused by both correlation and color of t he noises. The general results obtained in this Brief Report are appli ed to a bistable kinetic model. We find for the steady state of the mo del that in the case of correlated noises, the symmetry of SPD under t he reflection of the state variable x with respect to the origin is de stroyed. However in the case of non-Markovian processes driven by unco rrelated noises, the above symmetry is preserved.