IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v25y2005i3p621-627.html
   My bibliography  Save this article

Localization of periodic orbits of polynomial vector fields of even degree by linear functions

Author

Listed:
  • Starkov, Konstantin E.

Abstract

This paper is concerned with the localization problem of periodic orbits of polynomial vector fields of even degree by using linear functions. Conditions of the localization of all periodic orbits in sets of a simple structure are obtained. Our results are based on the solution of the conditional extremum problem and the application of homogeneous polynomial forms of even degrees. As examples, the Lanford system, the jerky system with one quadratic monomial and a quartically perturbed harmonic oscillator are considered.

Suggested Citation

  • Starkov, Konstantin E., 2005. "Localization of periodic orbits of polynomial vector fields of even degree by linear functions," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 621-627.
  • Handle: RePEc:eee:chsofr:v:25:y:2005:i:3:p:621-627
    DOI: 10.1016/j.chaos.2004.11.052
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077904007568
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2004.11.052?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. Starkov, Konstantin E. & Krishchenko, Alexander P., 2005. "Localization of periodic orbits of polynomial systems by ellipsoidal estimates," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 981-988.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhou, Xiaobing & Wu, Yue & Li, Yi & Wei, Zhengxi, 2008. "Hopf bifurcation analysis of the Liu system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1385-1391.
    2. Barrio, Roberto & Blesa, Fernando, 2009. "Systematic search of symmetric periodic orbits in 2DOF Hamiltonian systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 560-582.
    3. Ramos, J.I., 2006. "Determination of periodic orbits of nonlinear oscillators by means of piecewise-linearization methods," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1306-1313.

    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. Starkov, Konstantin E. & Starkov, Konstantin K., 2007. "Localization of periodic orbits of the Rössler system under variation of its parameters," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1445-1449.
    2. Barrio, Roberto & Blesa, Fernando, 2009. "Systematic search of symmetric periodic orbits in 2DOF Hamiltonian systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 560-582.
    3. Starkov, Konstantin E., 2009. "Bounds for a domain containing all compact invariant sets of the system describing the laser–plasma interaction," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1671-1676.

    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:25:y:2005:i:3:p:621-627. 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.