Limit cycles in 4-star-symmetric planar piecewise linear systems

Claudio A. Buzzi, Joao C. Medrado, Joan Torregrosa

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9 Citations (Scopus)


© 2019 Elsevier Inc. Our interest is centered in the study of the number of limit cycles for nonsmooth piecewise linear vector fields on the plane when the switching curve is xy=0. We consider the symmetric case. That is, one vector field defined in the odd quadrants and the other in the even ones. We deal with equilibrium points of center-focus type, with matrices in real Jordan form, in each vector field when the infinity is monodromic. In this case, we provide the center classification at infinity, we prove that the maximum order of a weak focus is five. Moreover, we show the existence of systems exhibiting five limit cycles bifurcating from infinity.
Original languageEnglish
Pages (from-to)2414-2434
JournalJournal of Differential Equations
Issue number5
Publication statusPublished - 1 Jan 2019


  • 4-cross-symmetric
  • Center-focus problem
  • Cyclicity
  • Limit cycles
  • Non-smooth differential system


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