一类三次Kolmogorov系统的正平衡点的性态与极限环的分支实例

The Properties of the Positive Equilibrium Points of a Class of Cubic Kolmogorov System and Examples of the Bifurcation of the Limit Cycles

本文研究了一类三次Kolmogorov系统,对它的两个正平衡点的类型与其附近轨线的性态展开了分类研究.同时考虑了正平衡点(1,1)附近的极限环分支情况,通过作适当的变换以及运用计算机对焦点量的仔细计算,得出了该系统在小参数扰动下能够从(1,1)附近分支出3个极限环的结论.

In this paper,a class of cubic Kolmogorov system in which two positive equilibrium points are classified is investigated.At the same time,the orbit of two equilibrium point（1,1） and（2,2） are considered.Moreover,through the appropriate transformations and the careful calculation of the focal values,the system that can occur 3 limit cycles near the positive equilibrium poin（1,1） under the small parameters disturbances is obtained.