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Hopf Bifurcation Analysis for the van der Pol Equation with Discrete and Distributed Delays

Author

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  • Xiaobing Zhou
  • Murong Jiang
  • Xiaomei Cai

Abstract

We consider the van der Pol equation with discrete and distributed delays. Linear stability of this equation is investigated by analyzing the transcendental characteristic equation of its linearized equation. It is found that this equation undergoes a sequence of Hopf bifurcations by choosing the discrete time delay as a bifurcation parameter. In addition, the properties of Hopf bifurcation were analyzed in detail by applying the center manifold theorem and the normal form theory. Finally, some numerical simulations are performed to illustrate and verify the theoretical analysis.

Suggested Citation

  • Xiaobing Zhou & Murong Jiang & Xiaomei Cai, 2011. "Hopf Bifurcation Analysis for the van der Pol Equation with Discrete and Distributed Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-16, May.
    • Handle: RePEc:hin:jnddns:569141
    DOI: 10.1155/2011/569141
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    Cited by:

    1. Koumene Taffo, G.I. & Siewe Siewe, M. & Tchawoua, C., 2016. "Stability switches and bifurcation in a two-degrees-of-freedom nonlinear quarter-car with small time-delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 226-239.

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