Steady-state analysis of a bistable system subject to a coloured multiplicative noise and a white additive noise with coloured cross-correlated noises

The steady-state properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different values of noise correlation times \tau_1 and \tau_2. After introducing a dimensionless parameter R(R=\alpha/D, D is the intensity of the multiplicative noise and \alpha is the intensity of the additive noise), and performing the numerical computations, we find the following points: (1) For the case of R>1, \lambda (the intensity of correlation between additive and multiplicative noises), \tau_1 and \tau_2 can induce the stationary probability distribution (SPD) transition from bimodal to unimodal in structure, but for the cases of R\leq1, the bimodal structure is preserved; (2) \alpha can also induce the SPD transition from bimodal to unimodal in structure; (3) the bimodal structure of the SPD exhibits a symmetrical structure as D increases.