IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v120y2016icp1-11.html
   My bibliography  Save this article

Limit cycles bifurcating from a degenerate center

Author

Listed:
  • Llibre, Jaume
  • Pantazi, Chara

Abstract

We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of all cubic polynomial differential systems we prove that at most three limit cycles can bifurcate from the degenerate center. As far as we know this is the first time that a complete study up to second order in the small parameter of the perturbation is done for studying the limit cycles which bifurcate from the periodic orbits surrounding a degenerate center (a center whose linear part is identically zero) having neither a Hamiltonian first integral nor a rational one. This study needs many computations, which have been verified with the help of the algebraic manipulator Maple.

Suggested Citation

  • Llibre, Jaume & Pantazi, Chara, 2016. "Limit cycles bifurcating from a degenerate center," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 1-11.
  • Handle: RePEc:eee:matcom:v:120:y:2016:i:c:p:1-11
    DOI: 10.1016/j.matcom.2015.05.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475415001147
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2015.05.005?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. Giné, Jaume, 2016. "Center conditions for nilpotent cubic systems using the Cherkas method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 129(C), pages 1-9.
    2. Dias, Fabio Scalco & Llibre, Jaume & Valls, Claudia, 2018. "Polynomial Hamiltonian systems of degree 3 with symmetric nilpotent centers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 60-77.
    3. Lavinia Bîrdac & Eva Kaslik & Raluca Mureşan, 2022. "Dynamics of a Reduced System Connected to the Investigation of an Infinite Network of Identical Theta Neurons," Mathematics, MDPI, vol. 10(18), pages 1-17, September.

    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:matcom:v:120:y:2016:i:c:p:1-11. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.