IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i14p2988-2998.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113002409
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2013.03.023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    4. 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.
    5. 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.
    6. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:392:y:2013:i:14:p:2988-2998. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.