【摘要】 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)(1)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 ,论证了在R+2 ={ (x ,y) :x >0 ,y >0 }内极限环的存在唯一性及其稳定性更多还原

【Abstract】 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.更多还原