| 一类四次系统幂零中心焦点判定与极限环分支 |
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| 引用本文： | 徐玲,刘一戎.一类四次系统幂零中心焦点判定与极限环分支[J].丽水学院学报,2011,33(2):1-5. |
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| 作者姓名： | 徐玲 刘一戎 |
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| 作者单位： | 浙江师范大学,数理与信息工程学院,浙江金华321004 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 研究一类原点为幂零奇点的四次系统的中心焦点判定与极限环分支问题。对一类四次系统给出了计算原点拟Lyapunov常数的递推公式,且在计算机上用Mathmatica软件推导出该系统原点前10个拟Lyapunov常数,进而分别推导出原点为中心和最高细焦点的条件,并在此基础上得到了此系统的扰动系统在原点充分小的领域内恰有10个包围初等结点的极限环的结论。
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| 关 键 词： | 四次系统 幂零奇点 拟Lyapunov常数 中心焦点 原点 极限环分支 |
Criterion of Center-Focus and Limit Cycle Bifurcation for a Class of Quartic-order Nilpotent Singular Points |
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| Xu Ling,Liu Yirong.Criterion of Center-Focus and Limit Cycle Bifurcation for a Class of Quartic-order Nilpotent Singular Points[J].Journal of Lishui University,2011,33(2):1-5. |
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| Authors: | Xu Ling Liu Yirong |
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| Institution: | (College of Mathematics,Physics and Information Engineering,Zhejiang Normal University,Jinhua Zhejiang 321004,China) |
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| Abstract: | A class of quartic system is studied in this paper,in which origin is nilpotent singular point.A recursive formula is derived to computer quasi-Lyapunov constants using the recursive formula and computer system-mathematic,and the first ten quasi-lyapunov constants using the recursve formula and computer system-mathemstic,and the first ten quasi-tlyapunov conatants of the system are given.The conditions for origin to be a center and the highest degree fine focus are derived.Ten limit,cycles in which elementary node is surrounded in the neighborhood of origin are obtained when the system is perturbed finely. |
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| Keywords: | quartic system nilpotent singular point quasi-Lyapunov constant center-focus origin limit cycle bifurcation |
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