具有功能性反应函数为的捕食系统

本文给出了具有功能性反应函数为 x的捕食系统x=γx-δ x y-αx2 ,y=-sy+β x y-εy2的全局相图 .得到了两种群持续共存和捕食者种群必将灭绝的条件 .讨论了此系统唯一正平衡点的 Hopf分支 ,并证明了该点可以成为二阶不稳定细焦点 ,从而得到该系统有出现至少三个极限环的可能 .

The Predator-prey System Possessing Functional Response Function That Is 

This thesis shows the global phase diagram of the predator-prey system with possessing functional response function that is x, =γx-δxy-αx 2, =-sy+βxy-εy 2. It gives the extinctive conditions of two animal community continuing coexistence and predator-prey animal community, and discusses the Hopf bifurcation of only positive equilibrium point in the system. It is testifies that the point can become two degree unstable fine focus. As a result we get a conclusion that it is possible that there will appear at least three limit cycles in the system.