Piecewise linear differential systems without equilibria produce limit cycles?

Jaume Llibre, Marco Antonio Teixeira

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

Abstract

© 2016, Springer Science+Business Media Dordrecht. In this article, we study the planar piecewise differential systems formed by two linear differential systems separated by a straight line, such that both linear differential have no equilibria, neither real nor virtual. When the piecewise differential system is continuous, we show that the system has no limit cycles. But when the piecewise differential system is discontinuous, we show that it can have at most one limit cycle.
Original languageEnglish
Pages (from-to)157-164
JournalNonlinear Dynamics
Volume88
Issue number1
DOIs
Publication statusPublished - 1 Apr 2017

Keywords

  • Continuous piecewise linear differential systems
  • Discontinuous piecewise differential systems
  • Limit cycles

Fingerprint Dive into the research topics of 'Piecewise linear differential systems without equilibria produce limit cycles?'. Together they form a unique fingerprint.

Cite this