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.
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van Gils, S.A., Krupa, M. & Tchistiakov, V. Homoclinic Twist Bifurcation in a System of Two Coupled Oscillators. Journal of Dynamics and Differential Equations 12, 733–806 (2000). https://doi.org/10.1023/A:1009094505023
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DOI: https://doi.org/10.1023/A:1009094505023