Detection function method and its application to a perturbed quintic Hamiltonian system

被引:14
作者
Liu, ZR [1 ]
Qian, TF
Li, JB
机构
[1] Yunnan Univ, Dept Math, Kunming 650091, Peoples R China
[2] Yunnan Univ, Inst Appl Math, Kunming 650091, Peoples R China
[3] Northwestern Univ, Dept Math, Evanston, IL 60208 USA
[4] Kunming Univ Sci & Technol, Ctr Nonlinear Sci Studies, Kunming 650093, Yunnan, Peoples R China
关键词
D O I
10.1016/S0960-0779(00)00270-8
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We employ the methods of both qualitative analysis and numerical exploration to investigate the bifurcation of limit cycles of a perturbed quintic Hamiltonian system. With the help of the detection functions for the perturbed Hamiltonian system, we study the perturbation of a quintic Hamiltonian system with 25 finite singular points and 4 infinite singular points. We first classify the phase portraits of the unperturbed system and categorize the closed orbits, then obtain the detection functions for the perturbed system, from which the detection curves and the number and the distribution of limit cycles are obtained. As application examples, we numerically compute the detection curves and draw the distribution of limit cycles. It seems that our methods are very effective on the study of the bifurcation of limit cycles of quintic Hamiltonian systems. (C) 2001 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码:295 / 310
页数:16
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