On the study of limit cycles of a cubic polynomial system under \(\mathbb Z_{4}\)-equivariant quintic perturba\-tion
type: Item
instance of: scholarly article
title: On the study of limit cycles of a cubic polynomial system under \(\mathbb Z_{4}\)-equivariant quintic perturba\-tion
zbMATH Open document ID: 1092.34015
author: Xuanliang Liu
author: Yuhai Wu
author: Maoan Han
published in: Chaos, Solitons and Fractals
publication date: 2005-05-12T00:00:00Z
review text: The authors study the number and distribution of limit cycles of a perturbed cubic Hamiltonian system which has 5 centers and 4 saddle points. The stability theory of singular points and singular close orbits are applied to study the Hopf, homoclinic loop and heteroclinic loop bifurcation of such system under \(\mathbb{Z}_4\)-equivariant quintic perturbation. By computing the Lyapunov constants, the authors find that the perturbed system has at least 16 limit cycles. Further, combining the Hopf bifurcation method and heteroclinic bifurcation method, the authors obtain at least 14 limit cycles.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 37C80
zbMATH DE Number: 2167912
zbMATH Keywords: limit cycles
zbMATH Keywords: stability theory of singular points
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: Lyapunov constant
zbMATH Keywords: equivariant dynamical system
MaRDI profile type: Publication
full work available at URL: j.chaos.2004.09.079
OpenAlex ID: W2045922928
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DOI: 10.1016/J.CHAOS.2004.09.079
description: scientific article; zbMATH DE number 2167912