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Analysis of a Belyakov homoclinic connection with ℤ2-symmetry

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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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Authors and Affiliations

  1. Department of Mathematics, Fac. Ciencias Experimentales, University of Huelva, Avda. Tres de Marzo s/n, 21071, Huelva, Spain

    Antonio Algaba & Manuel Merino

  2. Department of Applied Mathematics II, E.S. Ingenieros, University of Sevilla, Camino de los Descubrimientos s/n, 41092, Sevilla, Spain

    Alejandro J. Rodríguez-Luis

Authors
  1. Antonio Algaba
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  2. Manuel Merino
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  3. Alejandro J. Rodríguez-Luis
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Correspondence to Alejandro J. Rodríguez-Luis.

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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

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