On the limit cycles of a quintic planar vector field

被引：0
作者：
Yu-hai Wu
Li-xin Tian
Mao-an Han
机构：
[1] Jiangsu University,Department of Mathematics
[2] Shanghai Normal University,Department of Mathematics
来源：
Science in China Series A: Mathematics | 2007年 / 50卷
关键词：
double homoclinic loop; Melnikov function; stability; bifurcation; limit cycles; configuration; 34C07; 34C23; 34C37; 37G15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper concerns the number and distributions of limit cycles in a Z2-equivariant quintic planar vector field. 25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation. It can be concluded that H(5) ⩾ 25 = 52, where H(5) is the Hilbert number for quintic polynomial systems. The results obtained are useful to study the weakened 16th Hilbert problem.
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页码：925 / 940
页数：15
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