IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v16y2005i09ns0129183105008023.html
   My bibliography  Save this article

Generating Chaotic Limit Cycles For A Complex Duffing–Van Der Pol System Using A Random Phase

Author

Listed:
  • YONG XU

    (Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P. R. China)

  • WEI XU

    (Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P. R. China)

  • GAMAL M. MAHMOUD

    (Department of Mathematics, Faculty of Science, University of Assiut, 71516, Assiut, Egypt)

Abstract

Stochastic forces or random noises have been greatly used in studying the control of chaos of random real systems, but little is reported for random complex systems. Chaotic limit cycles of a complex Duffing–Van der Pol system with a random excitation is studied. Generating chaos via adjusting the intensity of random phase is investigated. We consider the positive top Lyapunov exponent as a criterion of chaos for random dynamical systems. It is computed based on the Khasminskii's formulation and the extension of Wedig's algorithm for linear stochastic systems. We demonstrate the stable behavior of deterministic system when noise intensity is zero by means of the top (local) Lyapunov exponent. Poincaré surface analysis and phase plot are used to confirm our results. Later, random noise is used to generate chaos by adjusting the noise intensity to make the top (local) Lyapunov exponent changes from a negative sign to a positive one, and the Poincaré surface analysis is also applied to verify the obtained results and excellent agreement between these results is found.

Suggested Citation

  • Yong Xu & Wei Xu & Gamal M. Mahmoud, 2005. "Generating Chaotic Limit Cycles For A Complex Duffing–Van Der Pol System Using A Random Phase," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(09), pages 1437-1447.
    • Handle: RePEc:wsi:ijmpcx:v:16:y:2005:i:09:n:s0129183105008023
    DOI: 10.1142/S0129183105008023
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183105008023
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0129183105008023?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.

    Citations

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


    Cited by:

    1. Xu, Yong & Xu, Wei & Mahmoud, Gamal M., 2008. "On a complex Duffing system with random excitation," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 126-132.
    2. Xu, Yong & Gu, Rencai & Zhang, Huiqing, 2011. "Effects of random noise in a dynamical model of love," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 490-497.
    3. Xu, Yong & Zhang, Huiqing & Xu, Wei, 2007. "On stochastic complex beam–beam interaction models with Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 259-272.

    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:wsi:ijmpcx:v:16:y:2005:i:09:n:s0129183105008023. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijmpc/ijmpc.shtml .

    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.