Bifurcations of limit cycles for a perturbed quintic Hamiltonian system with four infinite singular points

Hongxian Zhou; Wei Xu; Xiaoshan Zhao; Bingchang Zhou

doi:10.1016/j.amc.2006.08.174

Bifurcations of limit cycles for a perturbed quintic Hamiltonian system with four infinite singular points

Hongxian Zhou, Wei Xu, Xiaoshan Zhao, Bingchang Zhou

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

Abstract

By using the theory of bifurcations of dynamical systems and the method of detection function to investigate the bifurcation of limit cycles of a perturbed quintic Hamiltonian system with 25 finite singular points and four infinite singular points. From the detection functions for the perturbed system, we prove that under different determined parameter condition, the given system has at least 22 and 20 limit cycles and the configurations of compound eyes are also obtained.

Original language	English
Pages (from-to)	686-700
Number of pages	15
Journal	Applied Mathematics and Computation
Volume	187
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2006.08.174
State	Published - 15 Apr 2007

Keywords

Detection function
Hopf bifurcation
Limit cycle
Perturbed planar Hamiltonian systems

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10.1016/j.amc.2006.08.174

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title = "Bifurcations of limit cycles for a perturbed quintic Hamiltonian system with four infinite singular points",

abstract = "By using the theory of bifurcations of dynamical systems and the method of detection function to investigate the bifurcation of limit cycles of a perturbed quintic Hamiltonian system with 25 finite singular points and four infinite singular points. From the detection functions for the perturbed system, we prove that under different determined parameter condition, the given system has at least 22 and 20 limit cycles and the configurations of compound eyes are also obtained.",

keywords = "Detection function, Hopf bifurcation, Limit cycle, Perturbed planar Hamiltonian systems",

author = "Hongxian Zhou and Wei Xu and Xiaoshan Zhao and Bingchang Zhou",

year = "2007",

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T1 - Bifurcations of limit cycles for a perturbed quintic Hamiltonian system with four infinite singular points

AU - Zhou, Hongxian

AU - Xu, Wei

AU - Zhao, Xiaoshan

AU - Zhou, Bingchang

PY - 2007/4/15

Y1 - 2007/4/15

N2 - By using the theory of bifurcations of dynamical systems and the method of detection function to investigate the bifurcation of limit cycles of a perturbed quintic Hamiltonian system with 25 finite singular points and four infinite singular points. From the detection functions for the perturbed system, we prove that under different determined parameter condition, the given system has at least 22 and 20 limit cycles and the configurations of compound eyes are also obtained.

AB - By using the theory of bifurcations of dynamical systems and the method of detection function to investigate the bifurcation of limit cycles of a perturbed quintic Hamiltonian system with 25 finite singular points and four infinite singular points. From the detection functions for the perturbed system, we prove that under different determined parameter condition, the given system has at least 22 and 20 limit cycles and the configurations of compound eyes are also obtained.

KW - Detection function

KW - Hopf bifurcation

KW - Limit cycle

KW - Perturbed planar Hamiltonian systems

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DO - 10.1016/j.amc.2006.08.174

M3 - 文章

AN - SCOPUS:34247238710

SN - 0096-3003

VL - 187

SP - 686

EP - 700

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

Bifurcations of limit cycles for a perturbed quintic Hamiltonian system with four infinite singular points

Abstract

Keywords

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