LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER

被引:26
作者
Han, Maoan [1 ]
Jiang, Jiao [2 ]
Zhu, Huaiping [3 ]
机构
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[2] Shanghai Maritime Univ, Dept Math, Shanghai 200135, Peoples R China
[3] York Univ, Dept Math & Stat, Toronto, ON M3J 2R7, Canada
来源
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2008年 / 18卷 / 10期
基金
中国国家自然科学基金;
关键词
Near-Hamiltonian system; nilpotent center; Hopf bifurcation; limit cycle;
D O I
10.1142/S0218127408022226
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
As we know, Hopf bifurcation is an important part of bifurcation theory of dynamical systems. Almost all known works are concerned with the bifurcation and number of limit cycles near a nondegenerate focus or center. In the present paper, we study a general near-Hamiltonian system on the plane whose unperturbed system has a nilpotent center. We obtain an expansion for the first order Melnikov function near the center together with a computing method for the first coefficients. Using these coefficients, we obtain a new bifurcation theorem concerning the limit cycle bifurcation near the nilpotent center. An interesting application example - a cubic system having five limit cycles - is also presented.
引用
收藏
页码:3013 / 3027
页数:15
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