Dynamical properties of a bistable system driven by cross-correlated additive and multiplicative colored noises

The dynamical properties of a bistable system driven by additive and multiplicative colored noises with colored cross-correlation are investigated. Using the Novikov theorem and the projection operator method, we obtain the analytic expressions of the stationary probability distribution P-st(x), the relaxation time T-c, and the normalized correlation function C(s) of the system. The effects of the cross-correlation strength lambda and the cross-correlation time tau are discussed. By numerical computation, it is found that the cross-correlation strength vertical bar lambda vertical bar enhances the probability fluctuation of the dynamical variable and speeds up its decay; in particular, for the smaller values of vertical bar lambda vertical bar and the larger values of vertical bar lambda vertical bar, the correlation time tau plays opposite roles in slowing down and speeding up the probability fluctuation of the dynamical variable.