具有二次曲线解的Kolmogorov型三次系统的极限环

Limit Cycle for Cubic System of Kolmogorov Type with A Conic Solution

本文研究具有抛物轨线的Kolmogorov三次系统_3极限环的存在性,证明它在全平面上不存在极限环。在文献[9]—[11]的基础上,我们得到:具有二次曲线解的三次Kolmogorov系统在全平面上不存在极限环。

In this paper we study the existence of limit cycle for cubic system ()_3 of Kolmogorov type with a parabolic trajectory. We prove then there will not be any limit cycle on the full plane, and in Ref [9]-[11] he proved the non-existence of limit cycle of ()_3 with the integral curve of arbitrary elliptic or hyperbola. On the whole, we conclude: The cubic system of Kolmogorov type with conic solution on the whole plane has no limit cycle.