IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v28y2006i1p76-89.html
   My bibliography  Save this article

Classification of homoclinic tangencies for periodically perturbed systems

Author

Listed:
  • Tang, Yun
  • Yang, Fenghong
  • Chen, Guanrong
  • Zhou, Tianshou

Abstract

Classification of homoclinic tangencies for periodically perturbed systems is discussed. A relationship between the order of Melnikov function’s zeros and the harmonic components of a dynamical system is derived. By applying the singularity theory to the Melnikov function, possible types of homoclinic tangencies are studied for realization of the classification. In addition, certain multi-harmonically perturbed systems are investigated, showing the corresponding homoclinic bifurcation with their bifurcation diagrams.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:1:p:76-89
    DOI: 10.1016/j.chaos.2005.05.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790500487X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.05.004?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. Yang, Xiaoli & Xu, Wei & Sun, Zhongkui & Fang, Tong, 2005. "Effect of bounded noise on chaotic motion of a triple-well potential system," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 415-424.
    2. 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. 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. Chen, Zhen & Liu, X.B., 2015. "Effect of bounded noise on chaotic motions of stochastically perturbed slowly varying oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 72-81.
    3. Amer, Y.A., 2007. "Vibration control of ultrasonic cutting via dynamic absorber," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1703-1710.
    4. 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.
    5. 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.
    6. 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.
    7. 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:28:y:2006:i:1:p:76-89. 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.