| 李红伟,李锋,金银来.一类具有13个参数的7次系统的极限环分支[J].数学年刊A辑,2012,33(4):415~424 |
| 一类具有13个参数的7次系统的极限环分支 |
| Bifurcation of Limit Cycles in a Septic System with 13 Parameters |
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| DOI： |
| 中文关键词: 幂零奇点 中心-焦点问题 极限环分支 积分因子 拟Lyapunov常数 |
| 英文关键词:Nilpotent singular point, Center-focus problem, Bifurcation of
limit cycles, Integrating factor, Quasi-Lyapunov constant |
| 基金项目:国家自然科学基金(No.11071222);山东省自然科学基金(No.Y2008E22)资助的项目 |
| Author Name | Affiliation | E-mail | | LI Hongwei | Department of Mathematics,School of Science,Linyi University,Linyi 276005, Shandong,china | hongweifx@163.com | | LI Feng | Department of Mathematics,School of Science,Linyi University,Linyi 276005, Shandong,china | lf0539@126.com | | JIN Yinlai | Department of Mathematics,School of Science,Linyi University,Linyi 276005, Shandong,china | jinyinlai@lyu.edu.cn |
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| 中文摘要: |
| 研究了一类具有幂零奇点的7次多项式微分系统的极限环分支与中心问题.借助于数学软件MATHEMATICA,推导出系统在原点的前14个拟Lyapunov常数,从而得到了系统的原点为中心的充要条件,证明了系统在3阶幂零奇点处可以分支出14个极限环,给出了7次李雅谱诺夫系统在3阶幂零奇点处的环性数的下界. |
| 英文摘要: |
| In this paper, the bifurcation of limit cycles and the center conditions of a class
of septic polynomial differential systems with nilpotent singular points are investigated.
With the help of the mathematical software MATHEMATICA, the first 14 quasi-Lyapunov
constants at the origin of the system are deduced. As a result, necessary and sufficient
conditions for the origin of the system to be a center are obtained. The result that there exist
14 limit cycles created from the three-order nilpotent singular point is also proved. Moreover,
a lower bound of cyclicity of three-order nilpotent singular point for septic Lyapunov systems
is given. |
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