The state variable correlation function of the bistable system subject to the cross-correlated noises

The effects of correlations between additive and multiplicative noises on the state variable correlation function of a bistable system driven by cross-correlated noises were studied. Applying an approximate Fokker–Planck equation to the system, the analytic expression for the state variable correlation function of the system is derived by projection operator method. From numerical computations we find that the normalized correlation function C(s) decreases exponentially as the decay time s increases and decreases with increasing cross-correlated strength λ, however C(s) increases with increasing cross-correlated time τ. λ and τ play opposing roles in the C, i.e., λ enhances the rate of fluctuation decay of dynamical variable and the τ slows down the rate of fluctuation decay of dynamical variable.