An equivalent analytical method to deal with cross-correlated exponential type noises in the nonlinear dynamic system

Abstract

An equivalent analytical method to deal with cross-correlated exponential type noises in the nonlinear stochastic dynamical system is presented, which are equivalent to a linear combination of multiplicative white noises. This equivalent analytical method solves a recent conundrum which arose in the study of cross-correlated sine Wiener noises and provides a simple and effective method to deal with the related stochastic dynamical problem of exponential type noises. Applying this method, we investigate the FitzHugh-Nagumo dynamic system with a periodic signal and driven by cross-correlated sine-wiener noises, make steady-state analysis, and point out stochastic resonance phenomena induced by cross-correlated sine-wiener noises. We show the effects of the noise parameters on the stationary probability density and the Signal-to-Noise Ratio of the stochastic dynamical system. The cross-correlation time τ and the cross-correlation strength λ enhance the stochastic resonance excited by the additive sine Wiener noise η(t), in contrast, and inhibit the stochastic resonance excited by the multiplicative sine Wiener noise ε(t).