On the limit cycles of a quintic planar vector field

This paper concerns the number and distributions of limit cycles in a Z 2-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...

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Published inScience in China. Series A, Mathematics, physics, astronomy Vol. 50; no. 7; pp. 925 - 940
Main Authors Wu, Yu-hai, Tian, Li-xin, Han, Mao-an
Format Journal Article
LanguageEnglish
Published Department of Mathematics, Jiangsu University, Zhenjiang 212013, China%Department of Mathematics, Shanghai Normal University, Shanghai 200234, China 01.07.2007
Subjects
double homoclinic loop
bifurcation
Melnikov function
configuration
stability
limit cycles
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Summary:This paper concerns the number and distributions of limit cycles in a Z 2-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) 10878; 25 = 5, where H(5) is the Hilbert number for quintic polynomial systems. The results obtained are useful to study the weakened 16th Hilbert problem.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1006-9283
1862-2763
DOI:10.1007/s11425-007-0045-0