Lower bounds for the maximum number of limit cycles of discontinuous piecewise linear differential systems with a straight line of separation

J. Llibre, M. A. Teixeira, J. Torregrosa

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57 Citations (Scopus)

Abstract

In this paper, we provide a lower bound for the maximum number of limit cycles of planar discontinuous piecewise linear differential systems defined in two half-planes separated by a straight line. Here, we only consider nonsliding limit cycles. For those systems, the interior of any limit cycle only contains a unique equilibrium point or a unique sliding segment. Moreover, the linear differential systems that we consider in every half-plane can have either a focus (F), or a node (N), or a saddle (S), these equilibrium points can be real or virtual. Then, we can consider six kinds of planar discontinuous piecewise linear differential systems: FF, FN, FS, NN, NS, SS. We provide for each of these types of discontinuous differential systems examples with two limit cycles.

Original languageEnglish
Article number1350066
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume23
Issue number4
DOIs
Publication statusPublished - Apr 2013

Keywords

  • Limit cycle
  • Nonsmooth differential system
  • Piecewise linear differential system

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