中文摘要：

针对一类三次Kolmogorov捕食系统在正平衡点（1,1）的极限环分支问题,利用计算机代数系统Mathematica,将实系统逐步转化为复系统,计算伴随复系统的前5个奇点量,利用雅克比行列式推导正平衡点处可分支的极限环个数,得出该系统在一定条件下可分支5个小振幅极限环的结果。

英文摘要：

Aiming at bifurcations of limit cycles of a cubic Kolmogorov predator-prey system at the positive equilibrium point （ 1,1 ）, the real system is translated gradually into a complex system by the computer algebra system Mathematica, then the first five singular point values for the concomitant complex system are calculated, and the numbers of limit cycles at the positive equilibrium point can be deduced by Jacobi determinant. Five small amplitude limit cycles bifurcating from the positive equilibrium point can be concluded in the certain conditions.