Classification of the centers, their cyclicity and isochronicity for the generalized quadratic polynomial differential systems

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review

15 Citations (Scopus)

Abstract

In this paper we classify the centers, the cyclicity of their Hopf bifurcation and the isochronicity of the polynomial differential systems in R2 of degree d that in complex notation z = x + i y can be written asover(z, ̇) = (λ + i) z + (z over(z, -))frac(d - 2, 2) (A z2 + B z over(z, -) + C over(z, -)2), where d ≥ 2 is an arbitrary even positive integer, λ ∈ R and A, B, C ∈ C. Note that if d = 2 we obtain the well-known class of quadratic polynomial differential systems which can have a center at the origin. © 2009 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)427-437
JournalJournal of Mathematical Analysis and Applications
Volume357
Issue number2
DOIs
Publication statusPublished - 15 Sep 2009

Keywords

  • Centers
  • Cyclicity
  • Isochronous centers
  • Polynomial vector fields

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