文章基本信息

标题：Local bifurcation of limit cycles and center problem for a class of quintic nilpotent systems
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作者：Yusen Wu ; Luju Liu ; Feng Li 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2012
卷号：2012
期号：1
页码：45
DOI：10.1186/1687-1847-2012-45
语种：English
出版社：Hindawi Publishing Corporation
摘要：For a class of fifth degree nilpotent system, the shortened expressions of the first eight quasi-Lyapunov constants are presented. It is shown that the origin is a center if and only if the first eight quasi-Lyapunov constants are zeros. Under a small perturbation, the conclusion that eight limit cycles can be created from the eight-order weakened focus is vigorously proved. It is different from the usual Hopf bifurcation of limit cycles created from an elementary critical point. Mathematical Subject Classification: 34C07; 37G10.
关键词：quintic nilpotent system ; quasi-Lyapunov constant ; bifurcation of limit cycles ; center problem