Bifurcation of limit cycles from a four-dimensional center in control systems

Adriana Buicǎ, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

13 Citations (Scopus)


We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in a class of piecewise linear differential systems, which appears in a natural way in control theory. Our main result shows that three is an upper bound for the number of limit cycles, up to first-order expansion of the displacement function with respect to the small parameter. Moreover, this upper bound is reached. For proving this result we use the averaging method in a form where the differentiability of the system is not needed. © World Scientific Publishing Company.
Original languageEnglish
Pages (from-to)2653-2662
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number8
Publication statusPublished - 1 Jan 2005


  • Four-dimensional control system
  • Limit cycles
  • Piecewise linear differential systems


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