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The Focus-Center-Limit Cycle Bifurcation in Discontinuous Planar Piecewise Linear Systems Without Sliding

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Progress and Challenges in Dynamical Systems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 54))

Abstract

Planar discontinuous piecewise linear systems with two linearity zones, one of them being of focus type, are considered. By using an adequate canonical form under certain hypotheses, the bifurcation of a limit cycle, when the focus changes its stability after becoming a linear center, is completely characterized. Analytic expressions for the amplitude, period and characteristic multiplier of the bifurcating limit cycle are provided. The studied bifurcation appears in real world applications, as shown with the analysis of an electronic Wien bridge oscillator without symmetry.

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Acknowledgements

Authors acknowledge the fruitful suggestions of Prof. F. Torres on a preliminary version of the manuscript. They are partially supported by the Ministerio de Ciencia y Tecnología, Plan Nacional I+D+I, in the frame of projects MTM2009-07849, MTM2010-20907, MTM2012-31821, and by the Consejería de Educación y Ciencia de la Junta de Andalucía under grants TIC-0130 and P08-FQM-03770.

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Authors and Affiliations

  1. Departamento Matemática Aplicada II, E.T.S. Ingeniería, 41092, Sevilla, Spain

    Enrique Ponce, Javier Ros & Elísabet Vela

Authors
  1. Enrique Ponce
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  2. Javier Ros
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  3. Elísabet Vela
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Corresponding author

Correspondence to Enrique Ponce .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Oviedo, Oviedo, Spain

    Santiago Ibáñez

  2. Department of Mathematics, University of Oviedo, Oviedo, Spain

    Jesús S. Pérez del Río

  3. Department of Mathematics, University of Oviedo, Oviedo, Spain

    Antonio Pumariño

  4. Department of Mathematics, University of Oviedo, Oviedo, Spain

    J. Ángel Rodríguez

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Ponce, E., Ros, J., Vela, E. (2013). The Focus-Center-Limit Cycle Bifurcation in Discontinuous Planar Piecewise Linear Systems Without Sliding. In: Ibáñez, S., Pérez del Río, J., Pumariño, A., Rodríguez, J. (eds) Progress and Challenges in Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38830-9_21

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