摘要
焦点量的计算、中心条件的判定及极限环个数的研究是微分方程定性理论的热点问题。通过运用计算奇点量的方法来计算焦点量,对一类五次多项式微分系统在高次奇点的中心条件与极限环分支问题进行了研究。经过计算该系统奇点量的代数递推公式,得出该系统在原点前45个奇点量的表达式,推导出系统原点的中心判据并得到了该系统在高次奇点分支出7个极限环的实例。
In this article, Center condition and bifurcations of limit cycles at the degenerate critical point for a class of quintic polynomial system are investigated. Firstly, algebraic recursive formulas for computing singular point quantities of the origin are derived. The first 45th singular point values are given by using compute algebra Mathematica. Then the criterion of the origin being a center of this system is discussed. At last, we construct a quintic system which allows the appearance of seven limit cycles in the neighborhood of the origin.
出处
《桂林电子科技大学学报》
2007年第6期501-504,共4页
Journal of Guilin University of Electronic Technology
关键词
高次奇点
焦点量
奇点量
极限环分支
degenerate critical point
focal point value
singular point value
bifurcation of limit cycles
