具有二重抛物线解的二次系统  

On Quadratic System with a Two-fold Parabola Solution

作　　者：沈伯骞[1] 

机构地区：[1]辽宁师范大学数学系,大连116029

出　　处：《应用数学》2002年第4期43-46,共4页Mathematica Applicata

基　　金：辽宁省教委高校科研项目基金 (A990 3110 10 )

摘　　要：本文给出了具有二重抛物线解的二次系统的一般形状 ,并与具有单重抛物线解的二次系统相比较 ,证明了具有二重抛物线解的二次系统也有存在极限环的可能的 ,而且也是唯一的 ,但是二重抛物线解却是不可能成为二次系统的分界线不的 .A general form of the quadratic system with a two-fold parabola solution is given in this paper. We make a comparison between this system and the quadratic system with a single parabola solution. We proved that the former also exist limit cycle and at most one limit cycle, too. But the two-fold parabola solution can't become the separatrix cycle of the quadratic system.

关 键 词：二重抛物线解 二次系统 极限环 

分 类 号：O175.26[理学—数学]