Bifurcation of limit cycles from a two-dimensional center inside Rn

Jaume Llibre, Amar Makhlouf

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)


We study the bifurcation of limit cycles from the periodic orbits of a linear differential system in Rn perturbed inside a class of piecewise linear differential systems, which appears in a natural way in control theory. Our main result shows that at most one limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This upper bound is reached. For proving this result we use the averaging theory in a form where the differentiability of the system is not needed. © 2009 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)1387-1392
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number3-4
Publication statusPublished - 1 Feb 2010


  • Averaging method
  • Bifurcation
  • Control systems
  • Limit cycles


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