The number and distributions of limit cycles for a class of cubic near-Hamiltonian systems
type: Item
instance of: scholarly article
title: The number and distributions of limit cycles for a class of cubic near-Hamiltonian systems
zbMATH Open document ID: 1099.34032
author: Hong Zang
author: Tonghua Zhang
author: Maoan Han
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-03-29T00:00:00Z
review text: The paper concerns the number and distributions of limit cycles for a cubic Hamiltonian system under cubic perturbation which has 5 centers and 4 saddles. By using the idea of changing the stability of a homoclinic loop, it is proved that such system can have 9-11 limit cycles. The main result consists in finding two new distributions of 11 limit cycles for a cubic system. Such previous distributions are presented in the following works: 1. \textit{M. Han, Y. Wu} and \textit{P. Bi} [Discrete Contin. Dyn. Syst. 12, No. 4, 675--686 (2005; Zbl 1085.34027)]. 2. \textit{M. Han, T. Zhang} and \textit{H. Zang} [Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 12, 4285--4292 (2004; Zbl 1090.34025)].
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 5016210
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: limit cycle
zbMATH Keywords: Hilbert's 16th problem
zbMATH Keywords: homoclinic bifurcation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.04.085
OpenAlex ID: W4210804460
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DOI: 10.1016/J.JMAA.2005.04.085
description: scientific article; zbMATH DE number 5016210