Steady-state analysis of a bistable system with additive and multiplicative noises

An approximate Fokker-Planck equation for a general one-dimensional system driven by correlated noises is derived; the correlation times of the correlations between the noises are nonzero. The steady-state properties of the bistable kinetic model are analyzed. We find the following. (1) In the alpha-D parameter plane (alpha and D are the additive noise and multiplicative noise intensities, respectively), the area of the bimodal region of the stationary probability distribution (SPD) is contracted as lambda is increased (lambda is the strength of the correlations between noises), but the area of the bimodal region of the SPD is enlarged as tau is increased (tau is the correlation time of the correlations between noises). (2) lambda and tau play opposing roles in the transition of the SPD of the system. (3) For the case of perfectly correlated noises (lambda=1), there is not the phenomenon of the critical ratio (alpha/D=1) which was shown by Wu, Cao, and Re [Phys. Rev. E 50, 2496 (1994)]. (4) The change of the mean of the state variable is very remarkable in the small tau and large lambda regimes. (5) The normalized variance of the state variable increases with increasing tau, but decreases with increasing lambda.