Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model

    Research output: Contribution to journalArticleAcademicpeer-review

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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

    Cite this

    @article{70909173e4004ac283e97fa6e691cccf,
    title = "Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model",
    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.",
    keywords = "EWI-26246, Bogdanov–Takens bifurcation, MatCont, IR-97114, Homoclinic orbit, METIS-312705, Gray–Scott model",
    author = "Kouznetsov, {Iouri Aleksandrovitsj} and Meijer, {Hil Ga{\'e}tan Ellart} and {Al Hdaibat}, B. and W. Govaerts",
    note = "eemcs-eprint-26246",
    year = "2015",
    month = "8",
    doi = "10.1142/S0218127415501254",
    language = "Undefined",
    volume = "25",
    pages = "1550125",
    journal = "International journal of bifurcation and chaos in applied sciences and engineering",
    issn = "0218-1274",
    publisher = "World Scientific Publishing Co. Pte Ltd",
    number = "9",

    }

    Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model. / Kouznetsov, Iouri Aleksandrovitsj; Meijer, Hil Gaétan Ellart; Al Hdaibat, B.; Govaerts, W.

    In: International journal of bifurcation and chaos in applied sciences and engineering, Vol. 25, No. 9, 08.2015, p. 1550125.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model

    AU - Kouznetsov, Iouri Aleksandrovitsj

    AU - Meijer, Hil Gaétan Ellart

    AU - Al Hdaibat, B.

    AU - Govaerts, W.

    N1 - eemcs-eprint-26246

    PY - 2015/8

    Y1 - 2015/8

    N2 - 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.

    AB - 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.

    KW - EWI-26246

    KW - Bogdanov–Takens bifurcation

    KW - MatCont

    KW - IR-97114

    KW - Homoclinic orbit

    KW - METIS-312705

    KW - Gray–Scott model

    U2 - 10.1142/S0218127415501254

    DO - 10.1142/S0218127415501254

    M3 - Article

    VL - 25

    SP - 1550125

    JO - International journal of bifurcation and chaos in applied sciences and engineering

    JF - International journal of bifurcation and chaos in applied sciences and engineering

    SN - 0218-1274

    IS - 9

    ER -