The third order Melnikov function of a quadratic center under quadratic perturbations

Armengol Gasull, Adriana Buica, Jiazhong Yang

Research output: Contribution to journalArticleResearchpeer-review

15 Citations (Scopus)

Abstract

We study quadratic perturbations of the integrable system (1 + x) d H, where H = (x2 + y2) / 2. We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles. © 2006 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)443-454
JournalJournal of Mathematical Analysis and Applications
Volume331
DOIs
Publication statusPublished - 1 Jul 2007

Keywords

  • Bifurcation
  • High order Melnikov functions
  • Limit cycles
  • Quadratic systems

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