IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v298y2017icp141-152.html
   My bibliography  Save this article

Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center

Author

Listed:
  • Yang, Junmin
  • Yu, Pei

Abstract

In this paper, we study bifurcation of limit cycles in planar cubic near-Hamiltonian systems with a nilpotent center. We use normal form theory to compute the generalized Lyapunov constants and show that there exist at least 9 limit cycles around the nilpotent center. This is a new lower bound on the number of limit cycles in planar cubic near-Hamiltonian systems with a nilpotent center.

Suggested Citation

  • Yang, Junmin & Yu, Pei, 2017. "Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 141-152.
    • Handle: RePEc:eee:apmaco:v:298:y:2017:i:c:p:141-152
    DOI: 10.1016/j.amc.2016.11.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316306890
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.11.021?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. Yu, P. & Han, M., 2005. "Small limit cycles bifurcating from fine focus points in cubic order Z2-equivariant vector fields," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 329-348.
    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. Yu, P. & Han, M., 2006. "Limit cycles in generalized Liénard systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1048-1068.
    2. Singh, Vimal, 2008. "Novel frequency-domain criterion for elimination of limit cycles in a class of digital filters with single saturation nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 178-183.
    3. Wang, S. & Yu, P., 2005. "Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1317-1335.
    4. Wang, S. & Yu, P., 2006. "Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 606-621.
    5. Yu, P. & Han, M., 2007. "On limit cycles of the Liénard equation with Z2 symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 617-630.
    6. Singh, Vimal, 2007. "A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 813-816.
    7. Singh, Vimal, 2007. "Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1448-1453.
    8. Singh, Vimal, 2008. "Suppression of limit cycles in second-order companion form digital filters with saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 677-681.
    9. Giné, Jaume, 2007. "On some open problems in planar differential systems and Hilbert’s 16th problem," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1118-1134.
    10. Ting Huang & Jieping Gu & Yuting Ouyang & Wentao Huang, 2023. "Bifurcation of Limit Cycles and Center in 3D Cubic Systems with Z 3 -Equivariant Symmetry," Mathematics, MDPI, vol. 11(11), pages 1-22, June.
    11. Ye, Zhiyong & Han, Maoan, 2006. "Singular limit cycle bifurcations to closed orbits and invariant tori," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 758-767.

    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:apmaco:v:298:y:2017:i:c:p:141-152. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.