About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4

Stephanus A. van Gils, V. Tchistiakov, V. Tchistiakov

    Research output: Book/ReportReportProfessional

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    Abstract

    An algorithm to detect homoclinic twist bifurcation points in Z2 - symmetric autonomous systems of ordinary differential equations in R4 along curves of symmetric homoclinic orbits to hyperbolic equilibria has been developed. We show convergence of numerical approximations to homoclinic twist bifurcation points in such systems. A test function is defined on the homoclinic solutions, which has a regular zero in the codimensiontwo bifurcation points. This codimension-two singularity can be continued appending the test function to a three parameter vector field. We demonstrate the use of the test function on several examples of two coupled Josephson junctions.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversiteit Twente
    Number of pages25
    ISBN (Print)0169-2690
    Publication statusPublished - 1997

    Publication series

    NameMemorandum / Faculty of Applied Mathematics
    PublisherUniversity of Twente, Faculty of Applied Mathematics
    No.1371

    Keywords

    • METIS-141235
    • IR-30594

    Cite this

    van Gils, S. A., Tchistiakov, V., & Tchistiakov, V. (1997). About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4. (Memorandum / Faculty of Applied Mathematics; No. 1371). Enschede: Universiteit Twente.
    van Gils, Stephanus A. ; Tchistiakov, V. ; Tchistiakov, V. / About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4. Enschede : Universiteit Twente, 1997. 25 p. (Memorandum / Faculty of Applied Mathematics; 1371).
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    abstract = "An algorithm to detect homoclinic twist bifurcation points in Z2 - symmetric autonomous systems of ordinary differential equations in R4 along curves of symmetric homoclinic orbits to hyperbolic equilibria has been developed. We show convergence of numerical approximations to homoclinic twist bifurcation points in such systems. A test function is defined on the homoclinic solutions, which has a regular zero in the codimensiontwo bifurcation points. This codimension-two singularity can be continued appending the test function to a three parameter vector field. We demonstrate the use of the test function on several examples of two coupled Josephson junctions.",
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    note = "Memorandum fac. TW nr 1371",
    year = "1997",
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    isbn = "0169-2690",
    series = "Memorandum / Faculty of Applied Mathematics",
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    van Gils, SA, Tchistiakov, V & Tchistiakov, V 1997, About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4. Memorandum / Faculty of Applied Mathematics, no. 1371, Universiteit Twente, Enschede.

    About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4. / van Gils, Stephanus A.; Tchistiakov, V.; Tchistiakov, V.

    Enschede : Universiteit Twente, 1997. 25 p. (Memorandum / Faculty of Applied Mathematics; No. 1371).

    Research output: Book/ReportReportProfessional

    TY - BOOK

    T1 - About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4

    AU - van Gils, Stephanus A.

    AU - Tchistiakov, V.

    AU - Tchistiakov, V.

    N1 - Memorandum fac. TW nr 1371

    PY - 1997

    Y1 - 1997

    N2 - An algorithm to detect homoclinic twist bifurcation points in Z2 - symmetric autonomous systems of ordinary differential equations in R4 along curves of symmetric homoclinic orbits to hyperbolic equilibria has been developed. We show convergence of numerical approximations to homoclinic twist bifurcation points in such systems. A test function is defined on the homoclinic solutions, which has a regular zero in the codimensiontwo bifurcation points. This codimension-two singularity can be continued appending the test function to a three parameter vector field. We demonstrate the use of the test function on several examples of two coupled Josephson junctions.

    AB - An algorithm to detect homoclinic twist bifurcation points in Z2 - symmetric autonomous systems of ordinary differential equations in R4 along curves of symmetric homoclinic orbits to hyperbolic equilibria has been developed. We show convergence of numerical approximations to homoclinic twist bifurcation points in such systems. A test function is defined on the homoclinic solutions, which has a regular zero in the codimensiontwo bifurcation points. This codimension-two singularity can be continued appending the test function to a three parameter vector field. We demonstrate the use of the test function on several examples of two coupled Josephson junctions.

    KW - METIS-141235

    KW - IR-30594

    M3 - Report

    SN - 0169-2690

    T3 - Memorandum / Faculty of Applied Mathematics

    BT - About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4

    PB - Universiteit Twente

    CY - Enschede

    ER -

    van Gils SA, Tchistiakov V, Tchistiakov V. About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4. Enschede: Universiteit Twente, 1997. 25 p. (Memorandum / Faculty of Applied Mathematics; 1371).