IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v82y2012i9p1551-1571.html
   My bibliography  Save this article

Global dynamics of two coupled parametrically excited van der Pol oscillators

Author

Listed:
  • Wang, Xia
  • Chen, Fangqi

Abstract

Using a combination of analytical and numerical methods, the global bifurcations and chaotic dynamics of two non-linearly coupled parametrically excited van der Pol oscillators are investigated in detail. With the aid of the method of multiple scales, the slow flow equations are obtained. Based on the slow flow equations, normal form theory and the techniques of choosing complementary space are applied to find the explicit expressions of the simpler normal form associated with a double zero and a pair of pure imaginary eigenvalues. By the simpler normal form, using the global perturbation method developed by Kovacic and Wiggins, the analysis of global bifurcation and chaotic dynamics of two non-linearly coupled parametrically excited van der Pol oscillators is given. The results indicate that there exists a Silnikov type single-pulse homoclinic orbit for this class of system which implies the chaotic motions can occur. Numerical simulations are also given and verify the analytical predictions.

Suggested Citation

  • Wang, Xia & Chen, Fangqi, 2012. "Global dynamics of two coupled parametrically excited van der Pol oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1551-1571.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:9:p:1551-1571
    DOI: 10.1016/j.matcom.2012.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475412000456
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2012.02.006?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. Zhang, W. & Zu, J.W. & Wang, F.X., 2008. "Global bifurcations and chaos for a rotor-active magnetic bearing system with time-varying stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 586-608.
    2. Cao, D.X. & Zhang, W., 2008. "Global bifurcations and chaotic dynamics for a string-beam coupled system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 858-875.
    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. Zhang, Wei & Zu, Jean W., 2008. "Transient and steady nonlinear responses for a rotor-active magnetic bearings system with time-varying stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1152-1167.
    2. Inayat-Hussain, Jawaid I., 2009. "Geometric coupling effects on the bifurcations of a flexible rotor response in active magnetic bearings," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2664-2671.
    3. Cao, D.X. & Zhang, W., 2008. "Global bifurcations and chaotic dynamics for a string-beam coupled system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 858-875.
    4. Zhou, Liangqiang & Ji, Peng & Chen, Fangqi, 2021. "Chaos and subharmonic bifurcation of a composite laminated buckled beam with a lumped mass," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

    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:82:y:2012:i:9:p:1551-1571. 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: 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.