Bifurcation of limit cycles from a 4-dimensional center in 1:n resonance

Jaume Llibre, Amar Makhlouf

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7 Citations (Scopus)


We study the bifurcation of limit cycles from the periodic orbits of a linear differential system in R4 in resonance 1:n perturbed inside a class of piecewise linear differential systems, which appear in a natural way in control theory. Our main result shows that at most 1 limit cycle can bifurcate using expansion of the displacement function up to first order with respect to a 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 Inc. All rights reserved.
Original languageEnglish
Pages (from-to)140-146
JournalApplied Mathematics and Computation
Publication statusPublished - 1 Sept 2009


  • Averaging method
  • Bifurcation
  • Control systems
  • Limit cycles
  • Resonance 1:n


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