IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v32y2007i3p1059-1069.html
   My bibliography  Save this article

Limit cycles of a perturbed cubic polynomial differential center

Author

Listed:
  • Buică, Adriana
  • Llibre, Jaume

Abstract

In this paper we study the limit cycles of the system x˙=-y(x+a)(y+b)+εP(x,y), y˙=x(x+a)(y+b)+εQ(x,y) for ε sufficiently small, where a,b∈R⧹{0}, and P, Q are polynomials of degree n. We obtain that 3[(n−1)/2]+4 if a≠b and, respectively, 2[(n−1)/2]+2 if a=b, up to first order in ε, are upper bounds for the number of the limit cycles that bifurcate from the period annulus of the cubic center given by ε=0. Moreover, there are systems with at least 3[(n−1)/2]+2 limit cycles if a≠b and, respectively, 2[(n−1)/2]+1 if a=b.

Suggested Citation

  • Buică, Adriana & Llibre, Jaume, 2007. "Limit cycles of a perturbed cubic polynomial differential center," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1059-1069.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:3:p:1059-1069
    DOI: 10.1016/j.chaos.2005.11.060
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790501129X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.11.060?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. Asheghi, R. & Nabavi, A., 2020. "The third order melnikov function of a cubic integrable system under quadratic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Coll, Bartomeu & Llibre, Jaume & Prohens, Rafel, 2011. "Limit cycles bifurcating from a perturbed quartic center," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 317-334.

    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:3:p:1059-1069. 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.