Correlation Analysis Of The Solutions Of Two Types Of Predator Systems

There are complex relations among species in the biocoenosis.Due to the extensive application of the predator-prey model,so that more and more people are willing to study it deeply.In this paper,the solutions properties of two kinds of predator systems are studied by using nonlinear elliptic equation theory.The chapters which are discussed in this paper include the following parts.In Chapter 1,we outline biological meanings of functional response functions and the related research status of predation systems.Moreover,some common lemmas and basic knowledge which are relevant to the paper are given.In Chapter 2,we study the steady-state of the predator-prey model with Holling-III functional response under homogeneous Dirichlet boundary conditions.First of all,by means of calculating fixed point index of compact maps in cones,we can reduce the sufficient conditions of positive solutions.Moreover,the uniqueness and stability of positive solutions are determined by resorting to perturbation theory when m is sufficiently small.Then the existence,prolongation and stability of the local bifurcation solution from the semi-trivial solution are discussed by using bi-furcation theory.Finally,some numerical simulations are done to complement some analytical results.In Chapter 3,we discuss the predation system with Monod-Haldane func-tional response under homogeneous Dirichlet boundary conditions by using stability theory and bifurcation theory.First of all,prior estimates of positive solutions are given by using comparison principle.Then the asymptotic stability of trivial solu-tion and semi-trivial solutions are discussed combining stability theory and spectral analysis.Finally,combining Lyapunov-Schmidt method,we discuss the existence and stability of bifurcation solution from a double eigenvalue.Moreover,some an-notations are given.