IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v40y2009i5p2414-2429.html
   My bibliography  Save this article

Transition to chaos in the self-excited system with a cubic double well potential and parametric forcing

Author

Listed:
  • Litak, Grzegorz
  • Borowiec, Marek
  • Syta, Arkadiusz
  • Szabelski, Kazimierz

Abstract

We examine the Melnikov criterion for a global homoclinic bifurcation and a possible transition to chaos in case of a single degree of freedom nonlinear oscillator with a symmetric double well nonlinear potential. The system was subjected simultaneously to parametric periodic forcing and self-excitation via negative damping term. Detailed numerical studies confirm the analytical predictions and show that transitions from regular to chaotic types of motion are often associated with increasing the energy of an oscillator and its escape from a single well.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2414-2429
    DOI: 10.1016/j.chaos.2007.10.041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907009150
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.10.041?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.

    References listed on IDEAS

    as
    1. Litak, Grzegorz & Syta, Arkadiusz & Borowiec, Marek, 2007. "Suppression of chaos by weak resonant excitations in a non-linear oscillator with a non-symmetric potential," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 694-701.
    2. 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.
    3. Cao, Hongjun, 2005. "Primary resonant optimal control for homoclinic bifurcations in single-degree-of-freedom nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1387-1398.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tang, Yun & Yang, Fenghong & Chen, Guanrong & Zhou, Tianshou, 2006. "Classification of homoclinic tangencies for periodically perturbed systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 76-89.
    2. 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).
    3. Ario, Ichiro, 2013. "Multiple duffing problem in a folding structure with hill-top bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 51(C), pages 52-63.
    4. Litak, Grzegorz & Syta, Arkadiusz & Borowiec, Marek, 2007. "Suppression of chaos by weak resonant excitations in a non-linear oscillator with a non-symmetric potential," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 694-701.
    5. Amer, Y.A., 2007. "Vibration control of ultrasonic cutting via dynamic absorber," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1703-1710.
    6. El-Bassiouny, A.F., 2006. "Single-mode control and chaos of cantilever beam under primary and principal parametric excitations," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1098-1121.
    7. Siewe, M. Siewe & Cao, Hongjun & Sanjuán, Miguel A.F., 2009. "On the occurrence of chaos in a parametrically driven extended Rayleigh oscillator with three-well potential," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 772-782.
    8. Feng, Jingjing & Zhang, Qichang & Wang, Wei, 2012. "Chaos of several typical asymmetric systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 950-958.
    9. 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.
    10. El-Bassiouny, A.F., 2009. "On methods for continuous systems with quadratic, cubic and quantic nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1308-1316.

    More about this item

    Statistics

    Access and download statistics

    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:chsofr:v:40:y:2009:i:5:p:2414-2429. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.