Bifurcation of limit cycles from a polynomial degenerate center

Adriana Buicǎ, Jaume Giné, Jaume Llibret

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

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
Volume10
Issue number3
DOIs
Publication statusPublished - 1 Jan 2010

Keywords

  • Degenerate center
  • Limit cycles
  • Polynomial differential system

Fingerprint

Dive into the research topics of 'Bifurcation of limit cycles from a polynomial degenerate center'. Together they form a unique fingerprint.

Cite this