二次系统存在三次曲线弓形分界线环的充要条件

A Necccssary and Sufficient Condition for the Existence of Cubic Curve Sepratrix Cycle by A Bow Form in A Quadratic System

可证二次系统内含焦点的三次曲线弓形分界线环必由抛物线与直线所围成。定理1

This paper we proved that the cubic curve separatrix cycle by a bow form of quadratic system must constitute by a parabla and a straight line. We obtain the neccessary and sufficient condition for the existence of thus sepparatrix cycle in the general quadratic auadratic system, the Lotka--Volterra system and the of Ⅲ type system respectively.