The Hopf-van der Pol system: Failure of a homotopy method

Hil Gaétan Ellart Meijer, T. Kalmár-Nagy

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    Abstract

    The purpose of this article to provide an explicit example where continuation based on the homotopy method fails. The example is a one-parameter homotopy for periodic orbits between two well-known nonlinear systems, the normal form of the Hopf bifurcation and the van der Pol system. Our analysis shows that various types of obstructions can make approximation over the whole range of the homotopy parameter impossible. The Hopf-van der Pol system demonstrates that homotopy methods may fail even for seemingly innocent systems.
    Original languageUndefined
    Pages (from-to)323-328
    Number of pages6
    JournalDifferential equations and dynamical systems
    Volume20
    Issue number3
    DOIs
    Publication statusPublished - 2012

    Keywords

    • EWI-21066
    • Periodic orbits
    • IR-81397
    • Homotopy
    • METIS-296420
    • Global bifurcations

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