IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v179y2024ics0960077923013231.html
   My bibliography  Save this article

Repertoire of dynamical states in dissimilarly coupled Van der Pol oscillators

Author

Listed:
  • Manoranjani, M.
  • Subashree, B.
  • Senthilkumar, D.V.
  • Chandrasekar, V.K.

Abstract

We have considered dissimilarly coupled Van der Pol oscillators with an offset parameter which determines the degree of heterogeneity of the dissimilar coupling strength. Increasing degree of heterogeneity for decreasing values of the offset parameter results in a rich repertoire of bifurcation transitions and dynamical states including epochs of period doubling bifurcation. Two distinct multi-stable states are also observed along with several symmetry breaking dynamical states. We have deduced analytical stability conditions for Hopf and pitch-fork bifurcations through a linear stability analysis of symmetry preserving states, namely, trivial steady state and oscillation death state. The analytical conditions are found to match exactly with the simulation results in the two-parameter phase diagram. In addition to torus bifurcation, crisis and crisis induced intermittency routes to chaos are also observed for an appropriate heterogeneity of the dissimilar coupling strength. The period doubling bifurcation is characterized using the largest Lyapunov exponents of the dissimilarly coupled Van der Pol oscillators.

Suggested Citation

  • Manoranjani, M. & Subashree, B. & Senthilkumar, D.V. & Chandrasekar, V.K., 2024. "Repertoire of dynamical states in dissimilarly coupled Van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:chsofr:v:179:y:2024:i:c:s0960077923013231
    DOI: 10.1016/j.chaos.2023.114421
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923013231
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114421?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.

    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:179:y:2024:i:c:s0960077923013231. 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: 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.