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)


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.


Periodic Orbit Equilibrium Point Hopf Bifurcation Canonical Form Boundary Equilibrium 
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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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