Bifurcation of limit cycles from an n-dimensional linear center inside a class of piecewise linear differential systems

Pedro Toniol Cardin, Tiago De Carvalho, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

Let n be an even integer. We study the bifurcation of limit cycles from the periodic orbits of the n-dimensional linear center given by the differential system x1=-x2,x2=x1,⋯,x n-1=-xn,xn=xn-1, perturbed inside a class of piecewise linear differential systems. Our main result shows that at most (4n-6)n2-1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result we use the averaging theory in a form where the differentiability of the system is not needed. © 2011 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)143-152
JournalNonlinear Analysis, Theory, Methods and Applications
Volume75
Issue number1
DOIs
Publication statusPublished - 1 Jan 2012

Keywords

  • Averaging method
  • Bifurcation
  • Center
  • Control systems
  • Limit cycles
  • Piecewise linear differential systems

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