IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i18p2340-d639753.html
   My bibliography  Save this article

Assessing the Non-Linear Dynamics of a Hopf–Langford Type System

Author

Listed:
  • Svetoslav G. Nikolov

    (Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 4, 1113 Sofia, Bulgaria
    Department of Mechanics, University of Transport, Geo Milev Str. 158, 1574 Sofia, Bulgaria)

  • Vassil M. Vassilev

    (Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 4, 1113 Sofia, Bulgaria)

Abstract

In this paper, the non-linear dynamical behavior of a 3D autonomous dissipative system of Hopf–Langford type is investigated. Through the help of a mode transformation (as the system’s energy is included) it is shown that the 3D nonlinear system can be separated of two coupled subsystems in the master (drive)-slave (response) synchronization type. After that, based on the computing first and second Lyapunov values for master system, we have attempted to give a general framework (from bifurcation theory point of view) for understanding the structural stability and bifurcation behavior of original system. Moreover, a family of exact solutions of the master system is obtained and discussed. The effect of synchronization on the dynamic behavior of original system is also studied by numerical simulations.

Suggested Citation

  • Svetoslav G. Nikolov & Vassil M. Vassilev, 2021. "Assessing the Non-Linear Dynamics of a Hopf–Langford Type System," Mathematics, MDPI, vol. 9(18), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2340-:d:639753
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/18/2340/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/18/2340/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:9:y:2021:i:18:p:2340-:d:639753. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.