Homoclinic twist bifurcation in a system of two coupled oscillators

Stephan A. van Gils, Martin Krupa, Viktor Tchistiakov

    Research output: Contribution to journalArticleAcademicpeer-review

    4 Citations (Scopus)

    Abstract

    We analyse the dynamics of two identical Josephson junctions coupled through a purely capacitive load in the neighborhood of a degenerate symmetric homoclinic orbit. A bifurcation function is obtained applying Lin's version of the Lyapunov–Schmidt reduction. We locate in parameter space the region of existence of n-periodic orbits, and we prove the existence of n-homoclinic orbits and bounded nonperiodic orbits. A singular limit of the bifurcation function yields a one-dimensional mapping which is analyzed. Numerical computations of nonsymmetric homoclinic orbits have been performed, and we show the relevance of these computations by comparing the results with the analysis.
    Original languageEnglish
    Pages (from-to)733–80
    JournalJournal of dynamics and differential equations
    Issue number12
    DOIs
    Publication statusPublished - 2000

    Keywords

    • METIS-140539

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