一类三次幂零奇点的中心焦点判定与极限环分支  

Criterion of Center-focus and Limit Cycle Bifurcation for a Class of Three-order Nilpotent Singular Points

作　　者：卜珏萍[1] 赵倩倩[1] 毕先兵[1] 

机构地区：[1]中南大学数学科学与计算技术学院,湖南长沙410083

出　　处：《湖北民族学院学报（自然科学版）》2009年第3期293-297,共5页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：国家自然科学基金项目(10771196)

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Mathematica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.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.

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 

分 类 号：O125.13[理学—数学]