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The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems

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Abstract

The creation or destruction of a crossing limit cycle when a sliding segment changes its stability, is known as pseudo-Hopf bifurcation. In this paper, under generic conditions, we find an unfolding for such bifurcation, and we prove the existence and uniqueness of a crossing limit cycle for this family.

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Acknowledgements

The first author wishes to thank CONACyT for the support on the PhD Scholarship Number 320218. The second author is partially supported by MINECO Grants MTM2016-77278-P and MTM2013-40998-P, and AGAUR Grant Number 2014SGR-568, and the Grant FP7-PEOPLE-2012-IRSES 318999. The last author was supported by CONACyT Grant Number 180266.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Sonora, Hermosillo, Mexico

    Juan Castillo & Fernando Verduzco

  2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Catalonia, Spain

    Jaume Llibre

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  1. Juan Castillo
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  2. Jaume Llibre
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  3. Fernando Verduzco
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Correspondence to Fernando Verduzco.

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Castillo, J., Llibre, J. & Verduzco, F. The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems. Nonlinear Dyn 90, 1829–1840 (2017). https://doi.org/10.1007/s11071-017-3766-9

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  • DOI: https://doi.org/10.1007/s11071-017-3766-9

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