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

摘要

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.