Abstract
We study the existence, in a two-parameter plane, of double- and triple-pulse homoclinic orbits in a ℤ2-symmetric three-dimensional system, in the vicinity of a Belyakov point (a point where the involved equilibrium in the homoclinic connection changes from saddle to saddle-focus) in the Shil’nikov zone. The first-order computation of these global connections allows us to describe their position and organization in the parameter plane. The analytical results are successfully applied in the study of such degeneration in Chua’s equation.
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Algaba, A., Merino, M. & Rodríguez-Luis, A.J. Analysis of a Belyakov homoclinic connection with ℤ2-symmetry. Nonlinear Dyn 69, 519–529 (2012). https://doi.org/10.1007/s11071-011-0283-0
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DOI: https://doi.org/10.1007/s11071-011-0283-0