Classification of the centers, of their cyclicity and isochronicity for two classes of generalized quintic polynomial differential systems

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review

13 Citations (Scopus)

Abstract

In this paper we classify the centers localized at the origin of coordinates, the cyclicity of their Hopf bifurcation and their isochronicity for the polynomial differential systems in ℝ of degree d that in complex notation z = x + iy can be written as where j is either 0 or 1, d is an arbitrary odd positive integer greater than or equal to five, λ ε ℝ, and A,B,C,D ε ℂ. Note that if d = 5 we obtain special families of quintic polynomial differential systems. © 2009 Birkhäuser Verlag Basel/Switzerland.
Original languageEnglish
Pages (from-to)657-679
JournalNonlinear Differential Equations and Applications
Volume16
DOIs
Publication statusPublished - 1 Oct 2009

Keywords

  • Center
  • Cyclicity
  • Isochronous center
  • Polynomial vector fields

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