About Convergence of Numerical Approximations to Homoclinic Twist Bifurcation Points in Z2-Symmetric Systems in ℝ4

S.A. van Gils, V. Tchistiakov

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    Abstract

    An algorithm to detect homoclinic twist bifurcation points in Z2-symmetric autonomous systems of ordinary differential equations in ℝ4along curves of symmetric homoclinic orbits to hyperbolic equilibria hasbeen developed. We show convergence of numerical approximations to homoclinictwist bifurcation points in such systems. A test function is definedon the homoclinic solutions, which has a regular zero in the codimensiontwobifurcation points. This codimension-two singularity can be continuedappending the test function to a three parameter vector field. We demonstratethe use of the test function on several examples of two coupledJosephson junctions.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente
    Number of pages25
    Publication statusPublished - 1997

    Publication series

    NameMemorandum
    PublisherUniversity of Twente, Faculty of Applied Mathematics
    No.1371
    ISSN (Print)0169-2690

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