二次系统存在抛物线奇异环的充要条件

A Necessary and Sufficient Condition for the Existence of Parabolic Separatrix Cycles in a Quadratic System

迄今为止,对于二次系统存在除抛物线奇异环以外的所有各类二、三次曲线,甚至一些四次曲线分界线环或奇异环的充要条件已全部解决.本文将讨论二次系统存在抛物线奇异环的充要条件.并画出其所有可能的全局相图.

In this paper . we obtained a necessary and sufficient condition for the existence of parabolic separatrix cycles in a quadratic system, and drawed its all possible phase-portraits. Further we obtain an accurate parameter interval that a Ⅲ type system exist ltmit cycles.