HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS

被引：84
|
作者：
Han, Maoan [1 ]
Yang, Junmin [1 ]
Yu, Pei [2 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[2] Univ Western Ontario, Dept Appl Math, London, ON N6A 5B7, Canada
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2009年 / 19卷 / 12期
基金：
加拿大自然科学与工程研究理事会; 中国国家自然科学基金;
关键词：
Hopf cyclicity; Hamiltonian system; parameter; bifurcation; limit cycle; perturbation; LIMIT-CYCLE BIFURCATIONS; LIENARD SYSTEMS; PLANAR SYSTEM;
D O I：
10.1142/S0218127409025250
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider bifurcation of limit cycles in near-Hamiltonian systems. A new method is developed to study the analytical property of the Melnikov function near the origin for such systems. Based on the new method, a computationally efficient algorithm is established to systematically compute the coefficients of Melnikov function. Moreover, we consider the case that the Hamiltonian function of the system depends on parameters, in addition to the coefficients involved in perturbations, which generates more limit cycles in the neighborhood of the origin. The results are applied to a quadratic system with cubic perturbations to show that the system can have five limit cycles in the vicinity of the origin.
引用
收藏
页码：4117 / 4130
页数：14
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