Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory

Rebiha Benterki, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

9 Citations (Scopus)

Abstract

© 2016 Elsevier B.V. In this paper we classify the phase portraits in the Poincaré disc of the centers of the generalized class of Kukles systems ẋ=−y,ẏ=x+ax3y+bxy3, symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential systems of degree 4.
Original languageEnglish
Pages (from-to)273-283
JournalJournal of Computational and Applied Mathematics
Volume313
DOIs
Publication statusPublished - 15 Mar 2017

Keywords

  • Averaging method
  • Center
  • Generalized Kukles system
  • Limit cycle
  • Phase portrait

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