Limit cycles of discontinuous piecewise linear differential systems

Pedro Toniol Cardin, Tiago De Carvalho, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in n perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (resp. 3) 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 these results, we use the averaging theory in a form where the differentiability of the system is not needed. © 2011 World Scientific Publishing Company.
Original languageEnglish
Pages (from-to)3181-3194
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number11
Publication statusPublished - 1 Jan 2011


  • Discontinuous piecewise linear differential systems
  • averaging theory
  • limit cycles

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