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A general mechanism to generate three limit cycles in planar Filippov systems with two zones

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Abstract

Discontinuous piecewise linear systems with two zones are considered. A general canonical form that includes all the possible configurations in planar linear systems is introduced and exploited. It is shown that the existence of a focus in one zone is sufficient to get three nested limit cycles, independently on the dynamics of the another linear zone. Perturbing a situation with only one hyperbolic limit cycle, two additional limit cycles are obtained by using an adequate parametric sector of the unfolding of a codimension-two focus-fold singularity.

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Acknowledgments

Authors are partially supported by the Spanish Ministerio de Ciencia y Tecnologia, Plan Nacional I+D+I, in the frame of projects MTM2010-20907 and MTM2012-31821, and by the Consejería de Economía-Innovacíon-Ciencia-Empleo de la Junta de Andalucí a under grant P12-FQM-1658.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingeniería, Avda. de los Descubrimientos, 41092 , Sevilla, Spain

    Emilio Freire & Enrique Ponce

  2. Departamento de Matemática Aplicada, Escuela Politécnica Superior, Virgen de Africa, 7, 41011 , Sevilla, Spain

    Francisco Torres

Authors
  1. Emilio Freire
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  2. Enrique Ponce
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  3. Francisco Torres
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Correspondence to Enrique Ponce.

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Freire, E., Ponce, E. & Torres, F. A general mechanism to generate three limit cycles in planar Filippov systems with two zones. Nonlinear Dyn 78, 251–263 (2014). https://doi.org/10.1007/s11071-014-1437-7

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  • DOI: https://doi.org/10.1007/s11071-014-1437-7

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