一类食饵-捕食者系统的极限环

Limit Cycle of a Predator-prey System

对一类食饵 捕食者系统 (1)在ω >0和ω<0时进行了研究 .当ω >0时系统在第一象限内不存在极限环 .当ω <0 时讨论了系统平衡点的稳定性 ,系统无环的充分条件以及在第一象限围绕正平衡点存在惟一稳定极限环的条件 .

A class of predator-prey system (1) is studied when ω>0 and ω<0 respectively. The system has no limit cycle in the first quadrant when ω>0 . The stability of equilibrium, the sufficient conditions of nonexistence and conditions of the existence and uniqueness of the limit cycle around the positive equilibrium of the system in the first quadrant are probed when ω<0.