IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v32y2007i2p694-701.html
   My bibliography  Save this article

Suppression of chaos by weak resonant excitations in a non-linear oscillator with a non-symmetric potential

Author

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

Abstract

We examine the Melnikov criterion for transition to chaos in case of one degree of freedom non-linear oscillator with non-symmetric potential. This system, when subjected to an external periodic force, shows homoclinic transition from regular vibrations to chaos just before escape from a potential well. We focus especially on the effect of a second resonant excitation with a different phase on the system transition to chaos. We propose a way of its control.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:694-701
    DOI: 10.1016/j.chaos.2005.11.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905011021
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.11.026?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. 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)

    Citations

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


    Cited by:

    1. 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.
    2. 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.

    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. Amer, Y.A., 2007. "Vibration control of ultrasonic cutting via dynamic absorber," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1703-1710.
    3. 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.
    4. 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.
    5. 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:32:y:2007:i:2:p:694-701. 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.