IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v357y2005i3p383-396.html
   My bibliography  Save this article

Bifurcations and chaos in the triple-well Φ6-Van der Pol oscillator driven by external and parametric excitations

Author

Listed:
  • Siewe, M. Siewe
  • Kakmeni, F.M. Moukam
  • Tchawoua, C.
  • Woafo, P.

Abstract

The chaotic behavior of a nonlinear damped three-well Φ6-Van der Pol oscillator under external and parametric excitations is studied in detail by means of Melnikov's analysis. The predictions are tested against numerical simulations based on the basin of attraction of initial conditions. It is found that the threshold for the onset of chaos in the system increases as the amplitude of the parametric excitation decreases and increases as the amplitude of the external forcing increases. Additionally, the onset of chaos is studied through analysis of the Poincaré map, a construction of the bifurcation diagrams and a computation of the maximal Lyapunov exponent.

Suggested Citation

  • Siewe, M. Siewe & Kakmeni, F.M. Moukam & Tchawoua, C. & Woafo, P., 2005. "Bifurcations and chaos in the triple-well Φ6-Van der Pol oscillator driven by external and parametric excitations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(3), pages 383-396.
    • Handle: RePEc:eee:phsmap:v:357:y:2005:i:3:p:383-396
    DOI: 10.1016/j.physa.2005.06.070
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437105006370
    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.2005.06.070?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. Wu, Jianxin & Hong, Yiguang & Chen, Guanrong, 2009. "Occurrence and underlying mechanism of multi-stripe chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2250-2258.
    2. Ario, Ichiro, 2013. "Multiple duffing problem in a folding structure with hill-top bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 51(C), pages 52-63.
    3. Litak, Grzegorz & Borowiec, Marek & Syta, Arkadiusz & Szabelski, Kazimierz, 2009. "Transition to chaos in the self-excited system with a cubic double well potential and parametric forcing," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2414-2429.
    4. Yu, Yue & Zhang, Cong & Chen, Zhenyu & Lim, C.W., 2020. "Relaxation and mixed mode oscillations in a shape memory alloy oscillator driven by parametric and external excitations," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Feng, Jingjing & Zhang, Qichang & Wang, Wei, 2012. "Chaos of several typical asymmetric systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 950-958.

    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:357:y:2005:i:3:p:383-396. 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.