Associated Relaxation Time and the Correlation Function for a Bistable System with Coupling between Non-Gaussian and Gaussian Noise Terms

In this paper, we consider a bistable system with coupling between colored multiplicative non-Gaussian and additive Gaussian white noise terms, and study, the effects of the parameter q indicating the departure from the Gaussian noise and the correlation time tau of the colored multiplicative non-Gaussian noise oil the normalized correlation function C(s) and the associated relaxation time T-c by virtue of the projection operator method, in which the effects of the memory kernels of the correlation function are taken into account. The expressions of C(s) and T-c are obtained. It is found that, the parameter q enhances the fluctnation decay of the dynamical variable, while the correlation time tau slows down the fluctuation decay of the dynamical variable in the stationary, state. Numerical simulations are performed and are consistent with the approximate theoretical results.