Stability of bifurcating periodic solutions for van der Pol equation with continuous distributed delay

The van der Pol equation with continuous distributed time delay is given. Its linear stability is investigated by employing the Routh–Hurwitz criteria. Moreover, the local asymptotic stability conditions are also derived. By using the mean time delay as a bifurcation parameter, the model is found to...

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Bibliographic Details
Published in:Applied mathematics and computation 2003-12, Vol.146 (2), p.313-334
Main Authors: Liao, Xiaofeng, Wong, Kwok-wo, Wu, Zhongfu
Format: Article
Language:English
Subjects:
Continuous distributed delay
Exact sciences and technology
Hopf bifurcation
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Periodic solutions
Sciences and techniques of general use
Van der Pol equation
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Summary:The van der Pol equation with continuous distributed time delay is given. Its linear stability is investigated by employing the Routh–Hurwitz criteria. Moreover, the local asymptotic stability conditions are also derived. By using the mean time delay as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcations. The direction and the stability criteria of the bifurcating periodic solutions are obtained by applying the norm form theory and the center manifold theorem. Some numerical simulation examples for justifying the theoretical results are also given.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(02)00545-3