具有三次代数曲线解的五次系统的极限环

Limit Cycles of the Polynomial Systems of Degree 5 with Cubic Curve Solution

本文利用Maple软件强大的符号计算能力,得到了以 y=ax^3+bx^2+cx+d 为解的平面五次多项式系统的特征,由此证明了该系统在奇点的邻域内可以存在极限环。

In this paper, using the symbolic computation of Maple, the behavior of having the solution y = ax3 + bx2 + cx + d for the polynomlial systems of degree 5 are given. Further more, it is proved that there maybe have limit cycles in the neighborhood of singularity for the systems.