Numerical simulation study of the state variable correlation function of a bistable system subject to cross-correlated noises

We apply a numerical simulation method to study a normalized correlation function C(t) of a bistable system driven by cross-correlated noises. Based on a stochastic equivalent rule, we get a stochastic equivalent Stratonovich stochastic differential equation driven by Gaussian white noise for a bistable system driven by cross-correlated noises. Making use of a differential equation, C(t) was calculated by the numerical simulation procedure. Comparing C(t) calculated by the projection operator method of theoretics approximation to C(t) by the numerical simulation procedure, we find: (i) the difference in C(t) between the result of the theoretics approximation and that of the numerical simulation procedure is very small, i.e. the two results are approximately consistent; (ii) there is no difference in C(t) between the result of the theoretics approximation and the result of the numerical simulation procedure when the decay time t is large, i.e. they are entirely consistent; (iii) when the projection operator method is used to calculate C(t), the effects of higher orders of memory can be neglected