Qualitative Analysis On A Class Of Predator-prey Systems Possessing Functional Response Function X～(1/2)

In this thesis, we study a class of predator-prey system possessing functional response function x^1/2 which is a hybrid of cases from paper [4] and [5]。Firstly, we make the qualitative analysis on all equilibrium points of such a system, especially the high singular points and positive equilibrium points。Secondly, by using limit cycle theory and heteroclinic bifurcation theory, we study the existence and inexistence, as well as uniqueness of the limit cycles around the positive equilibrium points。Thirdly, we analyze the topological structure of the system in the first quadrant, and the behavior of critical points at infinity。Finally we explain in detail the population in the view of biology。...