二次系统(Ⅲ)_(n=0)的极限环

Limit Cycles of Quadratic System (Ⅲ)_(n=0)

利用一个时间变换,将二次系统(Ⅲ)n=0变为新系统(E)——它与二次系统(Ⅲ)n=0有相同的奇点O(0,0)和相同个数的包围O(0,0)的极限环,通过对系统(E)的研究,得到了二次系统(Ⅲ)n=0在O(0,0)外没有极限环的充分条件,由此,部分证明了叶彦谦在《多项式微分系统定性理论》中的一个猜想。

Through a time transformation, the quadratic system （Ⅲ）n=0 is changed into a new system （E）, which has the same singular point 0（0,0） and the same number of limit cycles around 0（0,0） with the system （Ⅲ）n=0. and then, a sufficient condition of the non-existence of limit cycles around 0（0,0） is obtained for the quadratic system （Ⅲ）n=0. Moreover a conjecture proposed in ＂Qualitative Theory of Polynomial Differential System＂ edited by Ye Yan-qian is partially confirmed.