Asymmetric effects on the associated relaxation time and the correlation function of a bistable system with correlated noises

The asymmetric effects on the associated relaxation time T-c and the correlation function C(s) of a bistable system are investigated. The stationary probability distribution (SPD) is derived, then the analytic expressions of T-c and C(s) are obtained. Under numerical computation, the results indicate: (i) the increasing of r (asymmetry parameter) can induce reentrance phenomenon in the SPD; (ii) the increasing of r can induce a one-peak structure on the T-c - R, T-c - D and T-c - lambda plots (R, D and lambda are the noise intensity ratio, multiplicative noise intensity and correlated intensity, respectively); (iii) there is a critical value of r, below it r enhances the fluctuation of the system, and above it r weakens the fluctuation of the system.