Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No Symmetry

Jaume Llibre, Enrique Ponce, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review

21 Citations (Scopus)

Abstract

© 2015, Springer Science+Business Media New York. Some techniques for proving the existence and uniqueness of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems with two and three zones and no symmetry. For planar systems with three linearity zones, the existence of two limit cycles surrounding the only equilibrium point at the origin is rigorously shown for the first time. The usefulness of the achieved analytical results is illustrated by considering non-symmetric memristor-based electronic oscillators.
Original languageEnglish
Pages (from-to)861-887
JournalJournal of Nonlinear Science
Volume25
Issue number4
DOIs
Publication statusPublished - 27 Aug 2015

Keywords

  • Limit cycles
  • Liénard piecewise linear differential systems
  • Nonlinear control systems
  • Periodic orbits

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