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Double Hopf Bifurcation For Stuart–Landau System With Nonlinear Delay Feedback And Delay-Dependent Parameters

Author

Listed:
  • SUQI MA

    (School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China)

  • QISHAO LU

    (School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China)

  • S. JOHN HOGAN

    (Department of Engineering Mathematics, University of Bristol, BS8 1TR, Bristol, United Kingdom)

Abstract

A Stuart–Landau system under delay feedback control with the nonlinear delay-dependent parametere-pτis investigated. A geometrical demonstration method combined with theoretical analysis is developed so as to effectively solve the characteristic equation. Multi-stable regions are separated from unstable regions by allocations of Hopf bifurcation curves in (p,τ) plane. Some weak resonant and non-resonant oscillation phenomena induced by double Hopf bifurcation are discovered. The normal form for double Hopf bifurcation is deduced. The local dynamical behavior near double Hopf bifurcation points are also clarified in detail by using the center manifold method. Some states of two coexisting stable periodic solutions are verified, and some torus-broken procedures are also traced.

Suggested Citation

  • Suqi Ma & Qishao Lu & S. John Hogan, 2007. "Double Hopf Bifurcation For Stuart–Landau System With Nonlinear Delay Feedback And Delay-Dependent Parameters," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 423-448.
    • Handle: RePEc:wsi:acsxxx:v:10:y:2007:i:04:n:s0219525907001227
    DOI: 10.1142/S0219525907001227
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