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The instability probability density evolution of the bistable system driven by Gaussian colored noise and white noise

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  • Guo, Yong-Feng
  • Wei, Fang
  • Xi, Bei
  • Tan, Jian-Guo

Abstract

In this paper, we studied the instability probability density evolution of the bistable system driven by Gaussian colored noise and white noise. Firstly, the bistable system is linearized in the initial area by applying Ω expansion theory of the Green function. Next, the time-dependent non-stationary state solutionpx,t of the Fokker–Planck equation for the linearized system is obtained by using eigenvalue and eigenvector theory. Finally, the effect of the time t, the colored noise intensity α, the correlation time τ and the white noise intensity D on p(x,t) are analyzed. Numerical computation results show that: p(x,t) is a monotonic decreasing function of variable x and intensity α. In contrast,p(x,t) is a monotonic increasing function of correlation time τ. Moreover, p(x,t) appears a peak with the increasing of t when x or D are fixed values respectively.

Suggested Citation

  • Guo, Yong-Feng & Wei, Fang & Xi, Bei & Tan, Jian-Guo, 2018. "The instability probability density evolution of the bistable system driven by Gaussian colored noise and white noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 200-208.
    • Handle: RePEc:eee:phsmap:v:503:y:2018:i:c:p:200-208
    DOI: 10.1016/j.physa.2018.02.208
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    References listed on IDEAS

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    1. Yong Xu & Jinzhong Ma & Haiyan Wang & Yongge Li & Jürgen Kurths, 2017. "Effects of combined harmonic and random excitations on a Brusselator model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(10), pages 1-7, October.
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    3. Yong Xu & Juanjuan Li & Jing Feng & Huiqing Zhang & Wei Xu & Jinqiao Duan, 2013. "Lévy noise-induced stochastic resonance in a bistable system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(5), pages 1-7, May.
    4. Xu, Yong & Wu, Juan & Du, Lin & Yang, Hui, 2016. "Stochastic resonance in a genetic toggle model with harmonic excitation and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 91-100.
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    Cited by:

    1. Pan, Yan & Ren, Yuhao & Duan, Fabing, 2018. "Noise benefits to robust M-estimation of location in dependent observations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 144-152.

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