有常数放养率的食饵——捕食者相互作用系统

The Predator-Preg Interacting System That Builted Foods Have Constant Breeding Rate

运用Liapunov第二方法，研究了有常数放养率的食饵－捕食者相互作用系统{x↑.=f(x)-φ（x）τ（y)＋H，y↑.=-eh(y)+Kh(y)φ（x)唯一正平衡点的稳定性。并利用Poincare-Bendixon环域定理、张芷芬唯一性定理及Hopf分支问题的Friedrich方法，论证了R2^+＝{(x,y):x>0,y>0}内极限环的存在唯一性及其稳定性。

By utilizing Liapunov’s second methods, we discussed steadiness of unique positive balanced points in the predator preg interacting system that buited foods have the constant breeding rate. This system is =f(x)-φ(x)τ(y)+H, =-eh(y)+Kh(y)φ(x).It is proved that the system existed an unique and steady limit cycle in R + 2=｛(x,y):x>0,y>0｝.For this purpose, we made use of Poincare bendixin cycle field theorem and Zhang Zhifeng unique theorem.