| 一类三次幂零奇点的中心焦点判定与极限环分支 |
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| 引用本文： | 卜珏萍,赵倩倩,毕先兵.一类三次幂零奇点的中心焦点判定与极限环分支[J].湖北民族学院学报(哲学社会科学版),2009,27(3). |
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| 作者姓名： | 卜珏萍 赵倩倩 毕先兵 |
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| 作者单位： | 中南大学数学科学与计算技术学院,湖南长沙,410083 |
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| 基金项目： | 国家自然科学基金项目 |
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| 摘 要： | 研究了一类原点为三次幂零奇点的三次微分系统.对一类三次系统给出了计算原点拟Lyapunov常数的递推公式,并在计算机上用Mathematics推导出该系统原点的前6个拟Lyapunov常数,进而推导出原点成为中心和最高阶细焦点的条件,并在此基础上得到了对系统作适当的微小扰动时,在原点充分小的邻域内恰有6个包围原点的极限环的结论.
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| 关 键 词： | 三次系统 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 Three-order Nilpotent Singular Points |
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| BU Jue-ping,ZHAO Qian-qian,BI Xian-bing.Criterion of Center-focus and Limit Cycle Bifurcation for a Class of Three-order Nilpotent Singular Points[J].Journal of Hubei Institute for Nationalities(Natural Sciences),2009,27(3). |
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| Authors: | BU Jue-ping ZHAO Qian-qian BI Xian-bing |
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| Institution: | Institute of Mathematical Science and Computing Technique;Central South University;Changsha 410083;China |
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| Abstract: | A class of cubic differential system is studied in this paper,in which origin is nilpotent singular point.A recursive formula is derived to compute quasi-Lyapunov constant.Using the recursive formula and computer system-mathematica,the first six quasi-Lyapunov constants of the system are given.The conditions for origin to be a center and the highest degree fine focus are derived.Six limit cycles in which origin is surrounded in the neighborhood of origin are obtained when the system is perturbed finely. |
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| Keywords: | cubic system nilpotent singular point quasi-Lyapunov constant center-focus origin limit cycle bifurcation |
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