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.
出处
《湖北民族学院学报（自然科学版）》
CAS
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)
