New results on averaging theory and applications

Murilo R. Cândido, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)


© 2016, Springer International Publishing. The usual averaging theory reduces the computation of some periodic solutions of a system of ordinary differential equations, to find the simple zeros of an associated averaged function. When one of these zeros is not simple, i.e., the Jacobian of the averaged function in it is zero, the classical averaging theory does not provide information about the periodic solution associated to a non-simple zero. Here we provide sufficient conditions in order that the averaging theory can be applied also to non-simple zeros for studying their associated periodic solutions. Additionally, we do two applications of this new result for studying the zero–Hopf bifurcation in the Lorenz system and in the Fitzhugh–Nagumo system.
Original languageEnglish
Article number106
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number4
Publication statusPublished - 1 Aug 2016


  • Averaging theory
  • Fitzhugh–Nagumo system
  • Lorenz system
  • Periodic solutions
  • Polynomial differential system


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