关于系统 =y,=(1-x^2)x+(α-x^2)y 的一些结果

Some Results on System x=y,y=(1-x^2)x+(α-x^2)y

本文考虑系统x=y y=(1—x^2)x+(a—x^2)y (1)给出下述结果(i)对 a>2,(1)的极限环包含三个奇点,且只有一个极限环.(ii)对1<a≤2,(1)的极限包含三个奇点,且至少有一个极限环.(iii)对 a≤0,(1)没有极限环.

In this paper we consider systemx=y,y=(1-x^2)x+(a-x^2)y (1)生and give some results as follows: (i) for a>2 any limit cycle of (1) must surround three singular points,and (1) has one and only one limit cycle.(ii) for 1<a≤2,any limit cycle of (1) must surround three singularpoints,and (1) has at lest one limit cycle. (iii) for a≤0. (1) has no limit cycle.