IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v34y2007i4p1307-1317.html
   My bibliography  Save this article

Approximating the amplitude and form of limit cycles in the weakly nonlinear regime of Liénard systems

Author

Listed:
  • López, J.L.
  • López-Ruiz, R.

Abstract

Liénard equations, x¨+ϵf(x)x˙+x=0, with f(x) an even continuous function are considered. In the weak nonlinear regime (ϵ→0), the number and O(ϵ0) approximation of the amplitude of limit cycles present in this type of systems, can be obtained by applying a methodology recently proposed by the authors [López-Ruiz R, López JL. Bifurcation curves of limit cycles in some Liénard systems. Int J Bifurcat Chaos 2000;10:971–80]. In the present work, that method is carried forward to higher orders in ϵ and is embedded in a general recursive algorithm capable to approximate the form of the limit cycles and to correct their amplitudes as an expansion in powers of ϵ. Several examples showing the application of this scheme are given.

Suggested Citation

  • López, J.L. & López-Ruiz, R., 2007. "Approximating the amplitude and form of limit cycles in the weakly nonlinear regime of Liénard systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1307-1317.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:4:p:1307-1317
    DOI: 10.1016/j.chaos.2006.04.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906003754
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.04.031?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.

    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:34:y:2007:i:4:p:1307-1317. 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: 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.