Stability Analysis Of Predator-prey Models With Functional Responses

The study of partial differential equation appeared firstly in the study of mathematical physics equation.Because of the important,scientific and potential application value,it has been widely applied to many fields.Reaction diffusion model is one of the important research of partial differential equations.With the development of the edge discipline mathematical biology,many reaction diffusion equations were used to study the population dynamics behavior.A predator-prey model with functional response is a research hotspot in recent years.It describes the trend of ecological species and predicts the survival process scientifically.The paper studies the existence and stability of multi-species predator-prey model with a diffuse functional response.The paper covers five parts:The first chapter is introduction.Principally this part introduces the biological background and the course of developing.Equilibrium solutions about a modified Leslie-Gower model are studied in the second chapter.Under the Neumann boundary condition,the existence and uniqueness of the model's constant solutions are studied.The constant solutions are given by Girolamo Cardano formula.The global asymptotic stability of the constant solutions is discussed by structing Lyapunov function.The stability is studied about a three species predator-prey model with BeddingtonDeAngelis functional response in the third chapter.Under the Neumann boundary condition,the uniform asymptotic stability of the semi trivial positive constant solution and the constant positive solution are given by the theory of the partial differential equation.The stability of a three-species predator-prey model with B-D functional response is studied in the fourth part.The existence and stability of the model's semi-trivial constant solutions are searched,and the global asymptotic stability is given by comparison principle.The existence and uniqueness of the model's constant positive solution are researched,then analysis their global asymptotic stability by energy integration method.The fifth chapter is to summarize the paper and present the further problems.