IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v62-63y2014ip1-9.html
   My bibliography  Save this article

Limit cycles of generalized Liénard polynomial differential systems via averaging theory

Author

Listed:
  • García, Belén
  • Llibre, Jaume
  • Pérez del Río, Jesús S.

Abstract

Using the averaging theory of first and second order we study the maximum number of limit cycles of the polynomial differential systemsẋ=y,ẏ=-x-ε(h1(x)+p1(x)y+q1(x)y2)-ε2(h2(x)+p2(x)y+q2(x)y2),which bifurcate from the periodic orbits of the linear center ẋ=y,ẏ=-x, where ε is a small parameter. If the degrees of the polynomials h1,h2,p1,p2,q1 and q2 are equal to n, then we prove that this maximum number is [n/2] using the averaging theory of first order, where [·] denotes the integer part function; and this maximum number is at most n using the averaging theory of second order.

Suggested Citation

  • García, Belén & Llibre, Jaume & Pérez del Río, Jesús S., 2014. "Limit cycles of generalized Liénard polynomial differential systems via averaging theory," Chaos, Solitons & Fractals, Elsevier, vol. 62, pages 1-9.
  • Handle: RePEc:eee:chsofr:v:62-63:y:2014:i::p:1-9
    DOI: 10.1016/j.chaos.2014.02.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077914000320
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2014.02.008?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.

    References listed on IDEAS

    as
    1. Chao Liu & Maoan Han, 2013. "The Number of Limit Cycles of a Polynomial System on the Plane," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, July.
    2. Llibre, Jaume & Valls, Clàudia, 2013. "Limit cycles for a generalization of polynomial Liénard differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 65-74.
    3. Yu, P. & Han, M., 2006. "Limit cycles in generalized Liénard systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1048-1068.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Asheghi, R. & Bakhshalizadeh, A., 2015. "Limit cycles in a Liénard system with a cusp and a nilpotent saddle of order 7," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 120-128.
    2. Xiong, Yanqin & Hu, Jianqiang, 2019. "A class of reversible quadratic systems with piecewise polynomial perturbations," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    3. Llibre, Jaume & Valls, Clàudia, 2013. "Limit cycles for a generalization of polynomial Liénard differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 65-74.

    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:62-63:y:2014:i::p:1-9. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.