具有二重抛物线解的二次系统

On Quadratic System with a Two-fold Parabola Solution

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.