Qualitative Analysis Of Two Types Of Predator Models

A differential equation model established to study the change regularity of biological systems,which is an important direction of the development of biomathe-matics,because the practical applications of biological models are very valuable,and it has been extensively studied by many experts.The Lotka-Volteera model is a kind of very important mathematical model.On this basis of many scholar continuously optimized the reaction function so as to make it more practical.In this paper,we mainly study the properties of solutions for two kinds of predator-prey models.A kind of predator-prey model with generalized Lotka-Volteer functional response function under Dirichlet boundary conditions is studied.Other kind is the predator-prey model of Monod-Haldane function with capture term.The main contents in this paper are as followsIn section 1,it is first use that maximum principle and Young inequality to get a priori estimates of model(1).Secondly by calculating the fixed point index and spec-trum analysis,we discussed the necessary and sufficient conditions for the existence of positive solutions of equilibrium equations and the dependence of coexistence for the parameter.In section 2,under the Dirichlet boundary conditions,by using the topological degree theory on the cone and the bifurcation theory,the existence,nonexistence,multiplicity,bifurcation and stability of the positive solutions of the second model are studied.