[1]丰建文,徐晨.关于Kukles系统弱问题[J].深圳大学学报理工版,2005,22(4):292-296.
 FENG Jian-wen,XU Chen.The weak problem for the Kukles system[J].Journal of Shenzhen University Science and Engineering,2005,22(4):292-296.
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关于Kukles系统弱问题()
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《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第22卷
期数:
2005年4期
页码:
292-296
栏目:
物理
出版日期:
2005-10-30

文章信息/Info

Title:
The weak problem for the Kukles system
文章编号:
1000-2618(2005)04-0292-05
作者:
丰建文徐晨
深圳大学理学院,深圳518060
Author(s):
FENG Jian-wenXU Chen
College of Science Shenzhen University Shenzhen 518060 P. R.China
关键词:
分岔函数扰动极限环哈密顿函数
Keywords:
Melnikov function Perturbation limit cycle Hamiltonian system
分类号:
O 175. 2
文献标志码:
A
摘要:
讨论与Kukles系统相关的弱问题,给出该系统的前四阶分岔函数表达式,证明了当前四阶分岔函数为零时,其后各阶分岔函数均为零,且该系统原点为中心;证明对于充分小的扰动参数,该系统的极限环的最小上界为3,同时给出该系统存在3个极限环的条件.
Abstract:
This study concerned the weak problem for the Kukles system. The expressions of the first four order Melnikov functions of the Kukles system were specified. Results prove that if the first four Melnikov functions Mj(h)=0 (j=1 ,2,3,4),then Mk(h)=0 for any k≥5 and the origin of the Kukles system is a centre. It is also shown that the lowest upper bound for the number of limit cycles for the perturbed system is equal to 3. The conditions of the lowest upper bound are given.
更新日期/Last Update: 2015-10-16