Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model

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    Abstract

    The second-order predictor for the homoclinic orbit is applied to the Gray–Scott model. The problem is used to illustrate the approximation of the homoclinic orbits near a generic Bogdanov–Takens bifurcation in n-dimensional systems of differential equations. In the process, we show that it is necessary to take (usually ignored) cubic terms in the Bogdanov–Takens normal form into account to derive a correct second-order prediction for the homoclinic bifurcation curve. The analytic solutions are compared with those obtained by numerical continuation.
    Original languageUndefined
    Pages (from-to)1550125
    Number of pages10
    JournalInternational journal of bifurcation and chaos in applied sciences and engineering
    Volume25
    Issue number9
    DOIs
    Publication statusPublished - Aug 2015

    Keywords

    • EWI-26246
    • Bogdanov–Takens bifurcation
    • MatCont
    • IR-97114
    • Homoclinic orbit
    • METIS-312705
    • Gray–Scott model

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