BISTABLE KINETIC-MODEL DRIVEN BY CORRELATED NOISES - STEADY-STATE ANALYSIS

A simple rule to obtain the Fokker-Planck equation for a general one-dimensional system driven by correlated Gaussian white noises is proved by the functional method. The Fokker-Planck equation obtained in this paper is applied to the bistable kinetic model. We find the following for the steady state. (1) In the alpha-D parameter plane (alpha is the strength of the additive noise and D is the multiplicative noise strength), the critical curve separating the unimodal and bimodal regions of the stationary probability distribution (SPD) of the model is shown to be affected by lambda, the degree of correlation of the noises. As lambda is increased, the area of the bimodal region in the alpha-D plane is contracted. (2) When we take a point fixed in the alpha-D plane and increase lambda, the form of the SPD changes from a bimodal to a unimodal structure. (3) The positions of the extreme value of the SPD of the model sensitively depend on the strength of the multiplicative noise, and weakly depend on the additive noise strength. (4) For lambda=1, the case of perfectly correlated noises, when the parameters alpha and D take values in the neighborhood of the line alpha=D in the alpha-D plane, the SPD's corresponding to the points alpha/D > 1 and alpha/D < 1 exhibit a very different shape of divergence. Therefore, the ratio alpha/D = 1 plays the role of a ''critical ratio.''