IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v248y2026icp17-25.html

Sewing limit cycles for piecewise smooth systems with two linear centers and a coupled rigid center

Author

Listed:
  • Batista, Warley M.
  • Llibre, Jaume
  • Tonon, Durval J.

Abstract

In this paper we provide an upper bound for the maximum number of limit cycles that two classes of planar piecewise smooth systems formed by three centers separated by two parallel lines can exhibit. So we have solved the extension of the 16th Hilbert problem for these two classes of piecewise smooth systems, that consists in providing a uniform upper bound for the maximum number of limit cycles that these two classes of differential systems can exhibit. The centers in the left and in the central parts are arbitrary linear centers, and the one on the right part is a rigid center ẋ=−y+xP(x,y),ẏ=x+yP(x,y), being the polynomial P(x,y) either λ+a10x+a01y or λ+a20x2+a11xy+a02y2, providing the two classes studied. In the first case the upper bound for the maximum number of limit cycles is eleven and in the second case such an upper bound is four.

Suggested Citation

  • Batista, Warley M. & Llibre, Jaume & Tonon, Durval J., 2026. "Sewing limit cycles for piecewise smooth systems with two linear centers and a coupled rigid center," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 248(C), pages 17-25.
    • Handle: RePEc:eee:matcom:v:248:y:2026:i:c:p:17-25
    DOI: 10.1016/j.matcom.2026.04.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475426001357
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2026.04.003?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

    for a different version of it.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:matcom:v:248:y:2026:i:c:p:17-25. 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.