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

Xiaobing Zhou, Murong Jiang and Xiaomei Cai

Discrete Dynamics in Nature and Society, 2011, vol. 2011, 1-16

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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:569141

DOI: 10.1155/2011/569141

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