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Double Hopf Bifurcation with Strong Resonances in Delayed Systems with Nonlinerities

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  • J. Xu
  • K. W. Chung

Abstract

An efficient method is proposed to study delay-induced strong resonant double Hopf bifurcation for nonlinear systems with time delay. As an illustration, the proposed method is employed to investigate the 1 : 2 double Hopf bifurcation in the van der Pol system with time delay. Dynamics arising from the bifurcation are classified qualitatively and expressed approximately in a closed form for either square or cubic nonlinearity. The results show that 1 : 2 resonance can lead to codimension-three and codimension-two bifurcations. The validity of analytical predictions is shown by their consistency with numerical simulations.

Suggested Citation

  • J. Xu & K. W. Chung, 2009. "Double Hopf Bifurcation with Strong Resonances in Delayed Systems with Nonlinerities," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-16, December.
    • Handle: RePEc:hin:jnlmpe:759363
    DOI: 10.1155/2009/759363
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