Linear estimate for the number of limit cycles of a perturbed cubic polynomial differential system

Jaume Llibre, Hao Wu, Jiang Yu

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

Perturbing the cubic polynomial differential systems over(x, ̇) = - y (a1 x + a0) (b1 y + b0), over(y, ̇) = x (a1 x + a0) (b1 y + b0) having a center at the origin inside the class of all polynomial differential systems of degree n, we obtain using the averaging theory of second order that at most 17 n + 15 limit cycles can bifurcate from the periodic orbits of the center. © 2007 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)419-432
JournalNonlinear Analysis, Theory, Methods and Applications
Volume70
DOIs
Publication statusPublished - 1 Jan 2009

Keywords

  • Averaging theory
  • Limit cycle
  • Polynomial differential system

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