Bifurcations of limit cycles in a perturbed quintic Hamiltonian system with six double homoclinic loops
type: Item
instance of: scholarly article
title: Bifurcations of limit cycles in a perturbed quintic Hamiltonian system with six double homoclinic loops
zbMATH Open document ID: 1159.34032
author: Yong-Xi Gao
author: Yuhai Wu
author: Lixin Tian
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2008-09-08T00:00:00Z
review text: The paper studies the number and distribution of limit cycles of a quintic planar Hamiltonian system subjected to a seven-degree perturbation. By means of numeric integral computation provided by Mathematica 4.1, at least 45 limit cycles are found by applying the method of double homoclinic loops bifurcation, Hopf bifurcation and qualitative analysis. The four configurations of 45 limit cycles of the system are presented. The results obtained may be useful in the study of the weakened 16th Hilbert problem.
reviewed by: Eugene Ershov
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 37B20
zbMATH DE Number: 5322535
zbMATH Keywords: limit cycles
zbMATH Keywords: Hilbert's 16th problem
zbMATH Keywords: double homoclinic loops
zbMATH Keywords: stability
zbMATH Keywords: near Hamiltonian planar system
zbMATH Keywords: Poincaré-Bendixson theorem
MaRDI profile type: Publication
full work available at URL: s10255-006-6154-7
OpenAlex ID: W1999625099
cites work: Bifurcation set and distribution of limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms
cites work: BIFURCATIONS OF LIMIT CYCLES IN A Z3-EQUIVARIANT VECTOR FIELD OF DEGREE 5
cites work: Q4789192
cites work: On the number of limit cycles in double homoclinic bifurcations
cites work: On the stability of double homoclinic and heteroclinic cycles.
cites work: The stability of double homoclinic loops.
cites work: Bifurcation of limit cycles near polycycles with \(n\) vertices
cites work: Some bifurcation methods of finding limit cycles
cites work: Cyclicity 1 and 2 conditions for a 2-polycycle of integrable systems on the plane
cites work: INVESTIGATIONS OF BIFURCATIONS OF LIMIT CYCLES IN Z2-EQUIVARIANT PLANAR VECTOR FIELDS OF DEGREE 5
cites work: Q4514346
cites work: Bifurcations of limit cycles in a \(Z_8\)-equivariant planar vector field of degree 7
cites work: Mathematical problems for the next century
cites work: Bifurcation set and distribution of limit cycles for a class of seven-order Hamiltonian system with fifteen-order perturbed terms
cites work: Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation
cites work: ON THE STUDY OF LIMIT CYCLES OF THE GENERALIZED RAYLEIGH–LIENARD OSCILLATOR
DOI: 10.1007/S10255-006-6154-7
description: scientific article; zbMATH DE number 5322535