Piecewise linear differential systems with only centers can create limit cycles?

Jaume Llibre, Marco Antonio Teixeira

Research output: Contribution to journalArticleResearchpeer-review

18 Citations (Scopus)


© 2017, Springer Science+Business Media B.V. In this article, we study the continuous and discontinuous planar piecewise differential systems formed only by linear centers separated by one or two parallel straight lines. When these piecewise differential systems are continuous, they have no limit cycles. Also if they are discontinuous separated by a unique straight line, they do not have limit cycles. But when the piecewise differential systems are discontinuous separated two parallel straight lines, we show that they can have at most one limit cycle, and that there exist such systems with one limit cycle.
Original languageEnglish
Pages (from-to)249-255
JournalNonlinear Dynamics
Issue number1
Publication statusPublished - 1 Jan 2018


  • Continuous piecewise linear differential systems
  • Discontinuous piecewise differential systems
  • First integrals
  • Limit cycles
  • Linear centers


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