Associated relaxation time and intensity correlation function of a bistable system driven by cross-correlation additive and multiplicative coloured noise sources

The associated relaxation time and the intensity correlation function of a bistable system driven by an additive and a multiplicative coloured noise with coloured cross-correlation are investigated. Using the Novikov theorem and the projection operator method, 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 are obtained. The effects of the noise intensity, the cross-correlation strength lambda and the cross-correlation time tau are discussed. By numerical computation, it is found that the cross-correlation strength |lambda| and the quantum noise intensity D decrease the relaxation of the system from unstable points. The cross-correlation time tau delays relaxation of the system from unstable points. The cross-correlation strength lambda and the cross-correlation time tau can alter the effects of the pump noise intensity Q. Thus, the relaxation time T-c is a stochastic resonant phenomenon, and distribution curves exhibit a single-maximum structure.