Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center

Jaume Llibre, Xiang Zhang

Research output: Contribution to journalArticleResearch

12 Citations (Scopus)

Abstract

© 2018 Elsevier Inc. From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles that this class of differential systems can have? Here we prove that when one of the linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles.
Original languageEnglish
Pages (from-to)537-549
JournalJournal of Mathematical Analysis and Applications
Volume467
DOIs
Publication statusPublished - 1 Nov 2018

Keywords

  • Discontinuous piecewise linear differential system
  • Limit cycle
  • Non-smooth differential system

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