平面齐次多项式系统的相图及平衡点的稳定性

Phase-portraits of plane homogeneouspolynomial systems and thestability of origin

多项式微分系统在动力系统研究中起着重要的作用，它是当前研究的主要方向之一。而系统在平衡点附近稳定性问题，更是人们关注的中心。文中对平面齐次多项式系统的平衡点的稳定性进行了分析并给出对应系统的全局相图及具体系统。

The global phase-portraits of plane homogeneous polynomial systems with odd degree n≤7, which are global stable, are given. The necessary and sufficient conditions for the global stability of these systems are derived. For n=3, detailed conditions are given.