Averaging analysis of a perturbated quadratic center

Jaume Llibre, Jesús S. Pérez del Río, José Angel Rodríguez

Research output: Contribution to journalArticleResearchpeer-review

65 Citations (Scopus)


It was proven that if the quadratic system inside the polynomial systems of degree n is perturbed, a first order in ε at most n limit cycles can be obtained. There are essentially three methods for studying the bifurcated limit cycles from a center. They are based on the Poincare return map, on the Poincare-Pontrjagin-Melkinov integrals or abelian integrals that are equivalent in the plane and on the inverse integrating factor. The averaging theory is used to study the bifurcated limit cycles.
Original languageEnglish
Pages (from-to)45-51
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number1
Publication statusPublished - 1 Oct 2001


  • Bifurcation from a center
  • Limit cycles


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