IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v229y2025icp743-757.html
   My bibliography  Save this article

Limit cycles in a class of planar discontinuous piecewise quadratic differential systems with a non-regular line of discontinuity (I)

Author

Listed:
  • He, Dongping
  • Llibre, Jaume

Abstract

In this paper we study the limit cycles which bifurcate from the periodic orbits of the quadratic uniform isochronous center ẋ=−y+xy, ẏ=x+y2, when this center is perturbed inside the class of all discontinuous piecewise quadratic polynomial differential systems in the plane with two pieces separated by a non-regular line of discontinuity, which is formed by two rays starting from the origin and forming an angle α=π/2. Using the Chebyshev theory we prove that the maximum number of hyperbolic limit cycles which can bifurcate from these periodic orbits is exactly 8 using the averaging theory of first order. For this class of discontinuous piecewise differential systems we obtain three more limit cycles than the line of discontinuity is regular, i.e., the case of where the two rays form an angle α=π.

Suggested Citation

  • He, Dongping & Llibre, Jaume, 2025. "Limit cycles in a class of planar discontinuous piecewise quadratic differential systems with a non-regular line of discontinuity (I)," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 743-757.
    • Handle: RePEc:eee:matcom:v:229:y:2025:i:c:p:743-757
    DOI: 10.1016/j.matcom.2024.10.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424004075
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.10.016?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.

    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:229:y:2025:i:c:p:743-757. 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.