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Planar Filippov Systems with Maximal Crossing Set and Piecewise Linear Focus Dynamics

  • Emilio FreireEmail author
  • Enrique Ponce
  • Francisco Torres
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 54)

Abstract

This paper includes some new results and a survey of known bifurcations for a family of Filippov systems. Such a family is constituted by planar piecewise linear systems with a discontinuity line where the crossing set is maximal and it has two dynamics of focus type. From the natural 12 parameters needed we obtain, under some generic conditions, a Liénard canonical form topologically equivalent to the original system with only four parameters. We describe, taking into account the number of equilibria inside each zone of linearity: zero, one or two, the qualitatively different phase portraits that can occur and the bifurcations connecting them.

Keywords

Periodic Orbit Equilibrium Point Hopf Bifurcation Canonical Form Boundary Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Authors are partially supported by the Ministerio de Ciencia y Tecnología, Plan Nacional \(I + D + I\), in the frame of projects MTM2009-07849, MTM2012-31821 and by the Consejería de Educación y Ciencia de la Junta de Andalucía under the gants TIC-0130 and P08-FQM-03770.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Emilio Freire
    • 1
    Email author
  • Enrique Ponce
    • 1
  • Francisco Torres
    • 1
  1. 1.Departamento Matemática Aplicada IIE.T.S. IngenieríaSevillaSpain

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