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Stochastic response of a ϕ6 oscillator subjected to combined harmonic and Poisson white noise excitations

Author

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  • Yue, Xiaole
  • Xu, Wei
  • Jia, Wantao
  • Wang, Liang

Abstract

The transient and stationary probability density functions (PDFs) of stochastic response of the ϕ6 Duffing oscillator under combined harmonic and external and parametric Poisson white noises excitations are investigated by the generalized cell mapping method in this paper. Based on the digraph analysis method, the global qualitative properties are obtained such as attractors, basins of attraction, basin boundaries, saddles and invariant manifolds. The evolutionary process of transient and stationary PDFs are shown based on the matrix analysis method. It is observed that there is a close relationship between evolutionary direction of PDF and the unstable manifold. Monte Carlo (MC) simulation is used to verify the accuracy of the matrix analysis method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:14:p:2988-2998
    DOI: 10.1016/j.physa.2013.03.023
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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. Han, Ping & Xu, Wei & Wang, Liang & Ma, Shichao, 2020. "The most probable response of some prototypical stochastic nonlinear dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. 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.
    4. Ren, Zhicong & Xu, Wei, 2020. "An improved path integration method for nonlinear systems under Poisson white noise excitation," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    5. Han, Qun & Xu, Wei & Sun, Jian-Qiao, 2016. "Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 115-125.
    6. Han, Qun & Xu, Wei & Hu, Bing & Huang, Dongmei & Sun, Jian-Qiao, 2018. "Extinction time of a stochastic predator–prey model by the generalized cell mapping method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 351-366.

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