一类四次系统的幂零中心条件与极限环分支

Conditions of Nilpotent Center and Limit Cycle Bifurcation for a Class of Special Quartic System

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.