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T-Points in a Z2-Symmetric Electronic Oscillator. (I) Analysis

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Abstract

In this work we study the presence of T-points, a kind of codimension-two heteroclinic loop, in a Z2-symmetric electronicoscillator. Our analysis proves that, in the parameter plane, whenthe equilibria involved are saddle-focus,three spiraling curves of global codimension-onebifurcations emerge from this T-point, corresponding tohomoclinic of the origin, homoclinic of the nontrivialequilibria and heteroclinic between the nontrivial equilibriaconnections. Some first-order features of these three curves are also shown.The analytical results, valid for all three-dimensionalZ2-symmetric systems, are successfully checked in themodified van der Pol–Duffing electronic oscillator considered.

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Authors and Affiliations

  1. Department of Applied Mathematics II, Escuela Superior Ingenieros, University of Sevilla, Camino de los Descubrimientos s/n, 41092, Sevilla, Spain

    F. Fernández-Sánchez, E. Freire & A. J. Rodríguez-Luis

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  1. F. Fernández-Sánchez
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  2. E. Freire
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  3. A. J. Rodríguez-Luis
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Fernández-Sánchez, F., Freire, E. & Rodríguez-Luis, A.J. T-Points in a Z2-Symmetric Electronic Oscillator. (I) Analysis. Nonlinear Dynamics 28, 53–69 (2002). https://doi.org/10.1023/A:1014917324652

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