基于中心流形的三维多项式微分系统极限环的存在性与稳定性

Existence and Stability of Three-Dimensional Polynomial Differential System Limit Cycles Based on Center Manifold

1963年,Sherman构造了三维多项式微分系统,并给出了周期解的存在性和稳定性条件.1989年,李德明等人用Liapunov-Schmidt reduction方法给出了此系统Hopf分支后周期解的存在性条件.本文将利用中心流形研究此系统极限环的存在性与稳定性.

In 1963,Sherman constructed a three-dimensional polynomial differential system,and gave the existence and stability of periodic solution.In 1989,Li Deming,etc.using Liapunov-Schmidt reduction method gives the system after the Hopf bifurcation of the existence conditions; this article will use the study center manifold existence and stability of this system limit cycle.