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

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  • Zhu, Ping

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).

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  • Zhu, Ping, 2021. "An equivalent analytical method to deal with cross-correlated exponential type noises in the nonlinear dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004781
    DOI: 10.1016/j.chaos.2021.111124
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    1. Ping, Zhu, 2023. "Analytical equivalent transformation method for nonlinear stochastic dynamics with multiple noises in high dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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