Double Hopf Bifurcation with Strong Resonances in Delayed Systems with Nonlinerities

J. Xu and K. W. Chung

Mathematical Problems in Engineering, 2009, vol. 2009, 1-16

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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:759363

DOI: 10.1155/2009/759363

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