Three nested limit cycles in discontinuous piecewise linear differential systems with two zones

Jaume Llibre, Enrique Ponce

Research output: Contribution to journalArticleResearchpeer-review

80 Citations (Scopus)

Abstract

In this paper we study a planar piecewise linear differential system formed by two regions separated by a straight line so that one system has a real unstable focus and the other a virtual stable focus which coincides with the real one. This system was introduced in a very recent paper (On the number of limit cycles in general planar piecewise linear systems, Discrete and Continuous Dynamical Systems-A 32, 2012, pp. 2147-2164) by S.-M. Huan and X.-S. Yang, who numerically showed that it can exhibit 3 limit cycles surrounding the real focus. This is the first example that a non-smooth piecewise linear differential system with two zones can have 3 nested limit cycles of crossing type surrounding a unique equilibrium. We provide a rigorous computer assisted proof of the quoted numerical result. Copyright © 2012 Watam Press.
Original languageEnglish
Pages (from-to)325-335
JournalDynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Volume19
Issue number3
Publication statusPublished - 28 May 2012

Keywords

  • Limit cycle
  • Non-Smooth differential system
  • Piecewise linear differential system

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