Bifurcation of limit cycles from a polynomial degenerate center

Adriana Buicǎ, Jaume Giné, Jaume Llibret

Research output: Contribution to journalArticleResearchpeer-review

12 Citations (Scopus)


Using Melnikov functions at any order, we provide upper bounds for the maximum number of limit cycles bifurcating from the period annulus of the degenerate center x = -y((x2 + y2)/2)m and y = x((x2 + y2)/2)m with m ≥ 1, when we perturb it inside the whole class of polynomial vector fields of degree n.The positive integers m and n are arbitrary. As far as we know there is only one paper that provide a similar result working with Melnikov functions at any order and perturbing the linear center x = - y, y = x.
Original languageEnglish
Pages (from-to)597-609
JournalAdvanced Nonlinear Studies
Issue number3
Publication statusPublished - 1 Jan 2010


  • Degenerate center
  • Limit cycles
  • Polynomial differential system


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