一类三次多项式系统的全局结构分析

摘要

研究一类三次多项式系统x=-y+a2x2y+a3xy2+ay3,y=x,通过分析无穷远奇点的性态以及轨线进入奇点的方向,得到了系统所有可能的全局结构相图.%In this paper, the cubic planar system (x)=-y+a3x2y+a3xy2+a4y3, (y)=-x is studied. The phase diagrams of global topological structure of the system are obtained by discussing behaviours of orbits near to singularites at infinity.