On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry

Jaume Llibre, Manuel Ordóñez, Enrique Ponce

Research output: Contribution to journalArticleResearchpeer-review

54 Citations (Scopus)

Abstract

Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems. New results are obtained for systems with three linearity zones without symmetry and having one equilibrium point in the central region. We also revisit the case of systems with only two linear zones giving shorter proofs of known results. A relevant application to the McKean piecewise linear model of a single neuron activity is included. © 2013 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)2002-2012
JournalNonlinear Analysis: Real World Applications
Volume14
Issue number5
DOIs
Publication statusPublished - 1 Oct 2013

Keywords

  • Liénard equation
  • Limit cycles
  • Piecewise linear systems

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