Classification of the centers, their cyclicity and isochronicity for a class of polynomial differential systems generalizing the linear systems with cubic homogeneous nonlinearities

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review

29 Citations (Scopus)

Abstract

In this paper we classify the centers, the cyclicity of its Hopf bifurcation and their isochronicity for the polynomial differential systems in R2 of arbitrary degree d ≥ 3 odd that in complex notation z = x + i y can be written asover(z, ̇) = (λ + i) z + (z over(z, -))frac(d - 3, 2) (A z3 + B z2 over(z, -) + C z over(z, -)2 + D over(z, -)3), where λ ∈ R and A, B, C, D ∈ C. If d = 3 we obtain the well-known class of all polynomial differential systems of the form a linear system with cubic homogeneous nonlinearities. © 2008 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)2192-2204
JournalJournal of Differential Equations
Volume246
DOIs
Publication statusPublished - 15 Mar 2009

Fingerprint Dive into the research topics of 'Classification of the centers, their cyclicity and isochronicity for a class of polynomial differential systems generalizing the linear systems with cubic homogeneous nonlinearities'. Together they form a unique fingerprint.

Cite this