摘要
本文研究了一类原点为三次幂零奇点的四次系统的中心焦点判定和极限环分支问题,给出了一类四次系统计算原点拟Lyapunov常数的递推公式,并得到了该系统原点的前9个拟Lyapunov常数b及原点成为中心和最高阶细焦点的充分必要条件,由此得到了该系统的扰动系统在原点充分小的邻域内恰有9个包围原点的极限环的结论.
A class of quartic differential system in which origin nilpotent singular point is studied in this paper.By a recursive formula,the first nine quasi-Lyapunov constants of the system are derived,from which the conditions for origin is a center and the highest degree fine focus are given.Correspondingly,by small perturbation,we prove that there exist nine small amplitude limit cycles in the neighborhood of the nilpotent singular point.
出处
《邵阳学院学报(自然科学版)》
2011年第1期14-19,共6页
Journal of Shaoyang University:Natural Science Edition
基金
国家自然科学基金项目(11071222)
关键词
四次系统
幂零奇点
拟Lyapunov常数
中心焦点问题
极限环分支
quartic system
nilpotent singular point
quasi-Lyapunov constants
center-focus problem
bifurcation of limit cycles