Limit cycles of polynomial differential equations with quintic homogeneous nonlinearities

Rebiha Benterki, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

9 Citations (Scopus)

Abstract

In this paper we mainly study the number of limit cycles which can bifurcate from the periodic orbits of the two centers ẋ=-y, ẏ=x; ẋ=-y(1-(x2+y2)2), ẏ=x(1-(x2+y2)2); when they are perturbed inside the class of all polynomial differential systems with quintic homogeneous nonlinearities. We do this study using the averaging theory of first, second and third orders. © 2013 Elsevier Ltd.
Original languageEnglish
Pages (from-to)16-22
JournalJournal of Mathematical Analysis and Applications
Volume407
Issue number1
DOIs
Publication statusPublished - 1 Nov 2013

Keywords

  • Averaging method
  • Center
  • Limit cycle
  • Periodic orbit
  • Reversible center

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