Effects of cross correlation on the relaxation time of a bistable system driven by cross-correlated noise

We study the effects of correlations between additive and multiplicative noise on relaxation time in a bistable system driven by cross-correlated noise. Using the projection-operator method, we derived an analytic expression for the relaxation time T(c) of the system, which is the function of additive (alpha) and multiplicative (D) noise intensities, correlation intensity lambda of noise, and correlation time tau of noise. After introducing a noise intensity ratio and a dimensionless parameter R=D/alpha, and then performing numerical computations, we find the following: (i) For the case of R<1, the relaxation time T(c) increases as R increases. (ii) For the cases of R>/=1, there is a one-peak structure on the T(c)-R plot and the effects of cross-correlated noise on the relaxation time are very notable. (iii) For the case of R<1, T(c) almost does not change with both lambda and tau, and for the cases of R>/=1, T(c) decreases as lambda increases, however T(c) increases as tau increases. lambda and tau play opposite roles in T(c), i.e., lambda enhances the fluctuation decay of dynamical variable and tau slows down the fluctuation decay of dynamical variable.