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A degenerate Hopf–saddle-node bifurcation analysis in a family of electronic circuits

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Abstract

This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achieved are applied to the study of a simple autonomous electronic circuit, which has just only one nonlinearity. The numerical results include the analysis of interesting resonance behaviors.

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Authors and Affiliations

  1. Department of Mathematics, Facultad de Ciencias, University of Huelva, Huelva, Spain

    A. Algaba, C. García & M. Merino

  2. Department of Applied Mathematics II, E. S. I., University of Sevilla, Sevilla, Spain

    E. Gamero

Authors
  1. A. Algaba
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  2. E. Gamero
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  3. C. García
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  4. M. Merino
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Correspondence to E. Gamero.

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Algaba, A., Gamero, E., García, C. et al. A degenerate Hopf–saddle-node bifurcation analysis in a family of electronic circuits. Nonlinear Dyn 48, 55–76 (2007). https://doi.org/10.1007/s11071-006-9051-y

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  • DOI: https://doi.org/10.1007/s11071-006-9051-y

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