IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i4p352-d496997.html
   My bibliography  Save this article

Dynamics of Rössler Prototype-4 System: Analytical and Numerical Investigation

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 dynamics of a 3D autonomous dissipative nonlinear system of ODEs-Rössler prototype-4 system, was investigated. Using Lyapunov-Andronov theory, we obtain a new analytical formula for the first Lyapunov’s (focal) value at the boundary of stability of the corresponding equilibrium state. On the other hand, the global analysis reveals that the system may exhibit the phenomena of Shilnikov chaos. Further, it is shown via analytical calculations that the considered system can be presented in the form of a linear oscillator with one nonlinear automatic regulator. Finally, it is found that for some new combinations of parameters, the system demonstrates chaotic behavior and transition from chaos to regular behavior is realized through inverse period-doubling bifurcations.

Suggested Citation

  • Svetoslav G. Nikolov & Vassil M. Vassilev, 2021. "Dynamics of Rössler Prototype-4 System: Analytical and Numerical Investigation," Mathematics, MDPI, vol. 9(4), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:352-:d:496997
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/4/352/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/4/352/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kuznetsov, A. & Afraimovich, V., 2012. "Heteroclinic cycles in the repressilator model," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 660-665.
    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. Rabajante, Jomar Fajardo & Talaue, Cherryl Ortega, 2015. "Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 166-182.

    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:4:p:352-:d:496997. 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: 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.