associated homogeneous equation

A class of quartic system,which is an accompany system of a quadratic differential one,is studied in this paper.

证明了它至多有一个极限环,并得到了奇点的性态和拓扑结构,把相伴系统的极限环的唯一性推广到了四次系统。

The article introduce the concept of accompany system of plane polynomial differential system, and study the similarities and differences about nonexistence, uniqueness of limit cycle and decision the centre or focus between the polynomial system and it′s accompany system.

引进平面多项式系统的相伴系统的概念 ,分析了多项式系统与其相伴系统之间在极限环不存在性 ,唯一性 ,中心焦点的判定等问题上的相似之处和不同之处 ,提出了几个公开问题 。