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 α-D parameter plane (α 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 λ is increased (λ is the strength of the correlations between noises), but the area of the bimodal region of the SPD is enlarged as τ is increased (τ is the correlation time of the correlations between noises). (2) λ and τ play opposing roles in the transition of the SPD of the system. (3) For the case of perfectly correlated noises (λ=1), there is not the phenomenon of the critical ratio (αD=1) which was shown by Wu, Cao, and Ke [Phys. Rev. E 50, 2496 (1994)]. (4) The change of the mean of the state variable is very remarkable in the small τ and large λ regimes. (5) The normalized variance of the state variable increases with increasing τ, but decreases with increasing λ.