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Nonlinear Dynamics

, Volume 78, Issue 1, pp 251–263 | Cite as

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

  • Emilio Freire
  • Enrique Ponce
  • Francisco Torres
Original Paper

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.

Keywords

Discontinuous piecewise linear systems Liénard equation Limit cycles 

Notes

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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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Emilio Freire
    • 1
  • Enrique Ponce
    • 1
  • Francisco Torres
    • 2
  1. 1.Departamento de Matemática AplicadaEscuela Técnica Superior de IngenieríaSevillaSpain
  2. 2.Departamento de Matemática AplicadaEscuela Politécnica SuperiorSevillaSpain

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