一类具有双中心的二次系统的Poincare分支

本文讨论了一类具有以弓形为边界的周期环域的二次系统的Ｐｏｉｎｃａｖｅ分支，证明了此分支至多能分支出两个极限环，并分别举出了二次系统恰好存在两个单重极限环；恰好存在一个二重极限环；恰好存在一个极限环和一个分界线环；不存在极限环但存在一个分界线环；以及从周期环域的弓形边界分支出两个极限环以及分支出一个二重极限环的例子

THE POINCARE BIFURCATION OF QUADRATIC SYSTEMS WITH DOUBLE CENTERS

We discuss the Poincare bifurcation of quadratic systems with two period regions in bow shaped bounds. We prove that at most two limit cycles occur from the bifurcation. we also give examples to show that there exist just two single limit cycles, or just one double limit cycle or just one single limit cycle and one separatrix cycle;or just one separatix cycle without any limit cycle. Further, we give an example to show that just two single limit cycles or one double limit cycle occur from the bow shaped bound of the period region.