Piecewise linear differential systems with two real saddles

Joan C. Artés, Jaume Llibre, Joao C. Medrado, Marco A. Teixeira

Research output: Contribution to journalArticleResearchpeer-review

63 Citations (Scopus)


In this paper we study piecewise linear differential systems formed by two regions separated by a straight line so that each system has a real saddle point in its region of definition. If both saddles are conveniently situated, they produce a transition flow from a segment of the splitting line to another segment of the same line, and this produces a generalized singular point on the line. This point is a focus or a center and there can be found limit cycles around it. We are going to show that the maximum number of limit cycles that can bifurcate from this focus is two. One of them appears through a Hopf bifurcation and the second when the focus becomes a node by means of the sliding. © 2013 IMACS.
Original languageEnglish
Pages (from-to)13-22
JournalMathematics and Computers in Simulation
Publication statusPublished - 1 Jan 2014


  • Hopf bifurcation
  • Limit cycle
  • Non-smooth differential system
  • Piecewise linear differential system
  • Sliding limit cycle


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