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Approximate Fokker–Planck equation of system driven by multiplicative colored noises with colored cross-correlation

Author

Listed:
  • Liang, G.Y.
  • Cao, L.
  • Wu, D.J.

Abstract

Using the Hanggi ansatz to truncate the evolution equation for probability density, an approximate Fokker–Planck equation (AFPE) is derived. This AFPE is valid for one-dimensional general systems driven by two multiplicative colored noises (τ1≠0 and τ2≠0) that are correlated in color (τ3≠0) under the condition for τ1,τ2, and τ3 to satisfy some inequalities. We apply this AFPE to a symmetrical bistable potential system driven by a colored multiplicative noise and a white additive noise with white cross-correlation. To verify the validity of our analytical approximation the numerical simulations for this system is performed. We discovered a new phenomenon that the symmetry of stationary probability density broken by the correlation between the noises can be gradually recovered as the noise self-correlation time is increased.

Suggested Citation

  • Liang, G.Y. & Cao, L. & Wu, D.J., 2004. "Approximate Fokker–Planck equation of system driven by multiplicative colored noises with colored cross-correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 371-384.
    • Handle: RePEc:eee:phsmap:v:335:y:2004:i:3:p:371-384
    DOI: 10.1016/j.physa.2003.12.023
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    Cited by:

    1. Liu, Jian & Qiao, Zijian & Ding, Xiaojian & Hu, Bing & Zang, Chuanlai, 2021. "Stochastic resonance induced weak signal enhancement over controllable potential-well asymmetry," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Zhang, Gang & Shu, Yichen & Zhang, Tianqi, 2022. "The study on dynamical behavior of FitzHugh–Nagumo neural model under the co-excitation of non-Gaussian and colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    3. 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).
    4. Zhang, Huiqing & Xu, Wei & Xu, Yong, 2009. "The study on a stochastic system with non-Gaussian noise and Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 781-788.
    5. Li, Wei & Zhang, Ying & Huang, Dongmei & Rajic, Vesna, 2022. "Study on stationary probability density of a stochastic tumor-immune model with simulation by ANN algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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