Two Categories With A Functional Response To A Prey - Predator Diffusion Model

In this thesis, we study two kinds of predator-prey models with Holling-II and Beddington-DeAngelis functional response. The diffusive phenomenon can be seen nearly everywhere in nature. It is important to research the global existence of solutiongs and the existence of traveling front solutions of the two kinds of diffusive models for us to exploit and reserve natural resource.There are five chapters in this thesis. In the first chapter, the important meaning of this paper is introduced; In the second chapter, some necessary knowledge is given. In the third chapter, for the first model, the diffusive predator-prey models with Holling-II functiongal response is studyed. Using the upper and lower solutions method, the uniform boundedess and global existence of solutions method, the uniform boundedess and global existence of solution to the predator-orey diffusion system. Meanwhile, sufficient conditions of the local asyptotical stability of the positive equilibrium point is given by linearization respectively. The global asymptotical stability of the unique positive equilibrium point is also given Lypunnov function. In the forth chapter, for the second model, we study the diffusive predator-prey models with Beddington-DeAngelis functional response is studyed and searched a traveling wave solution between two equilibrium points, in ecological meaning, then,the paper define a Wazewski set and examine an exit set. The property of the system nereby the equilibrium points can be known by linearing the system at these points, and the solution remains in a particular regin. At last, using a Lypunnov function in that region, the paper prove the existence of traveling front solutions undering some conditions. In the fifth chapter, a conclusion of this thesis is given.