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Multiple Hopf Bifurcations of Four Coupled van der Pol Oscillators with Delay

Author

Listed:
  • Liqin Liu

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

  • Chunrui Zhang

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

Abstract

In this paper, a system of four coupled van der Pol oscillators with delay is studied. Firstly, the conditions for the existence of multiple periodic solutions of the system are given. Secondly, the multiple periodic solutions of spatiotemporal patterns of the system are obtained by using symmetric Hopf bifurcation theory. The normal form of the system on the central manifold and the bifurcation direction of the bifurcating periodic solutions are derived. Finally, numerical simulations are attached to demonstrate our theoretical results.

Suggested Citation

  • Liqin Liu & Chunrui Zhang, 2023. "Multiple Hopf Bifurcations of Four Coupled van der Pol Oscillators with Delay," Mathematics, MDPI, vol. 11(23), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4831-:d:1291531
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    References listed on IDEAS

    as
    1. Acosta, A. & Gallo, R. & García, P. & Peluffo-Ordóñez, D., 2023. "Positive invariant regions for a modified Van Der Pol equation modeling heart action," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    2. Ngamsa Tegnitsap, J.V. & Fotsin, H.B. & Megam Ngouonkadi, E.B., 2021. "Magnetic coupling based control of a chaotic circuit: Case of the van der Pol oscillator coupled to a linear circuit," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Mussa Juane, Mariamo & García-Selfa, David & Muñuzuri, Alberto P., 2020. "Turing instability in nonlinear chemical oscillators coupled via an active medium," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
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