一个在无穷远点分支出6个极限环的三次多项式系统

来源期刊：中南大学学报(自然科学版)2004年第4期

论文作者：黄文韬 刘一戎

文章页码：690 - 693

关键词：三次多项式系统;奇点量;无穷远点;极限环分支

Key words：cubic polynomial system; singular point value; infinity; bifurcation of limit cycles

摘    要：研究了一类三次系统无穷远点的极限环分支问题。对一类三次系统给出了计算无穷远点奇点量的递推公式,并在计算机上用计算机代数系统Mathematica推导出该系统无穷远点的前6个奇点量,进而导出了无穷远点成为中心和最高阶细焦点的条件,在此基础上得到了一个三次系统在无穷远点分支出6个极限环的实例,指出了极限环的精确位置。

Abstract: The bifurcation of limit cycles at infinity for a class of cubic polynomial systems was studied in the paper. A recursive formula is derived to compute singular point values at infinity. Using the recursive formula and computer algebra system-Mathematica, the first six singular point values at infinity of the system are given. The conditions for infinity to be a center and the highest degree fine focus are derived, respectively. A cubic system that bifurcates six limit cycles from infinity is obtained. The exact positions of these limit cycles are also pointed out.