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Probabilistic response of dynamical systems based on the global attractor with the compatible cell mapping method

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Listed:
  • Yue, Xiaole
  • Xu, Yong
  • Xu, Wei
  • Sun, Jian-Qiao

Abstract

A generalized compatible cell mapping (CCM) method is proposed in this paper to take advantages of the simple cell mapping (SCM) method, the generalized cell mapping (GCM) method together with a subdivision procedure. A coarse cell partition is first used to obtain a covering set of the global attractor. Then, a finer global attractor is obtained by the subdivision process. The probabilistic response of stochastic dynamic systems is obtained by the sparse matrix analysis algorithm applied to the covering set of the global attractor. Because the computational domain is the covering set of the global attractor rather than the whole state space, the numerical efficiency of the proposed method can be greatly improved as compared to the GCM. A three-dimensional and a four-dimensional dynamical system under Poisson white noise excitation are studied to demonstrate the effectiveness of the proposed method for the probabilistic response analysis. Monte Carlo simulations show a good agreement with the proposed method.

Suggested Citation

  • Yue, Xiaole & Xu, Yong & Xu, Wei & Sun, Jian-Qiao, 2019. "Probabilistic response of dynamical systems based on the global attractor with the compatible cell mapping method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 509-519.
    • Handle: RePEc:eee:phsmap:v:516:y:2019:i:c:p:509-519
    DOI: 10.1016/j.physa.2018.10.034
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    References listed on IDEAS

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    1. Er, Guo-Kang, 1999. "A consistent method for the solution to reduced FPK equation in statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(1), pages 118-128.
    2. Yue, Xiaole & Xu, Wei & Jia, Wantao & Wang, Liang, 2013. "Stochastic response of a ϕ6 oscillator subjected to combined harmonic and Poisson white noise excitations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 2988-2998.
    3. Yue, Xiaole & Xu, Wei & Zhang, Ying & Du, Lin, 2018. "Analysis of global properties for dynamical systems by a modified digraph cell mapping method," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 206-212.
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    Citations

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    Cited by:

    1. Ma, Shichao & Wang, Liang & Ning, Xin & Yue, Xiaole & Xu, Wei, 2019. "Probabilistic responses of three-dimensional stochastic vibro-impact systems," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 308-314.
    2. Yue, Xiaole & Yu, Bei & Li, Yongge & Xu, Yong, 2022. "Dynamic response and bifurcation for Rayleigh-Liénard oscillator under multiplicative colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Yue, Xiaole & Lv, Ge & Zhang, Ying, 2021. "Rare and hidden attractors in a periodically forced Duffing system with absolute nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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