一类n+1次Kolmogorov系统的极限环

The limit cycle of a kind of n+l-degree Kolmogorov's system

对一类n+1次Kolmogorov系统进行了研究.当a_4>0时,系统在第一象限内不存在极限环;当a_4<0时,讨论了系统平衡点的稳定性态,系统无环的充分条件以及在第一象限内存在唯一稳定极限环的条件。

A kind of n+1-degree Kohnogorov's system is considered. The system has no limit cycle in the first quadrant when α4>0. The stability of equilibrium, the sufficient conditions of nonexistence and conditions of existence and the uniqueness of the stable limit cycle iii the first quadrant of this system are discussed when α4<0.