李锋,金银来.一类具幂零奇点的五次系统中心条件及极限环分支[J].数学研究及应用,2011,31(5):937~945
一类具幂零奇点的五次系统中心条件及极限环分支
Center Conditions and Bifurcation of Limit Cycles at Nilpotent Critical Point in a Quintic Lyapunov System
投稿时间:2010-05-09  最后修改时间:2010-11-20
DOI:10.3770/j.issn:1000-341X.2011.05.021
中文关键词:  三阶幂零奇点,中心-焦点问题,极限环分支,拟李雅普诺夫常数.
英文关键词:three-order nilpotent critical point  center-focus problem  bifurcation of limit cycles  quasi-Lyapunov constant.
基金项目:山东省自然科学基金(Grant No.Y2007A17)
作者单位
李锋 临沂大学理学院, 山东 临沂 276005 
金银来 临沂大学理学院, 山东 临沂 276005 
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中文摘要:
      本文研究了一类具有三次幂零奇点的五次系统的中心条件与极限环分支,得到了系统原点为中心的充要条件,并且证明了系统可以从原点分支出8个极限环,给出了具有三次幂零奇点的五次系统的极限环分支的下界.
英文摘要:
      In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 8 quasi Lyapunov constants are deduced. As a result, the necessary and sufficient conditions to have a center are obtained. The fact that there exist 8 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems.
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