Stability And The Optimal Harvesting Of Several Kinds Of Predator-prey Models

By revealing the dynamics behavior of the predator-prey model based on the basic ecological environment, and condition mathematical model proves some confusion of nature. Predator-prey model is a kind of mathematical models which are common.Predator-prey models propose the problems which influence the growth, the existence,stability of the species and so on. The equilibrium points, economical equilibrium points and optimal harvesting of the predator-prey model become one of the hot topics in the field of biology and mathematics. Based on the Lotka-Volterra model, this thesis use the theory of eigen value, the Hamiltonian function and Pontryagin maximum principle to study the stability of several kinds of predator-prey models with optimal harvesting,we achieve meaningful conclusions.According to the content of it, this thesis is divided into four chapters as follows:Chapter 1 This chapter introduces the main problems and background in this paper. of this paper.Chapter 2 This chapter study the stability and optimal harvesting of predator-prey model with disease in prey .We use eigen value theory to study the stability of the equilibrium points. On the basis of the model which is stable, we discuss the existence of bionomic equilibrium,and we construct the Hamiltonian function and use the Pontryagin maximum principle to solve the optimal harvesting.Chapter 3 This chapter study the stability and optimal harvesting of predator-prey model with imprecise parameters .We use the interval function to represent the uncertain parameters. By eigen value theory to analyze its stability, we discuss the existence of bionomic equilibrium, and we construct the Hamiltonian function and use the Pontryagin maximum principle to solve the optimal harvesting.Chapter 4 This chapter study the stability and optimal harvesting of predator-prey model for resource with reserve area.Firstly, we get the equilibrium of the model and analyse of its existence, by eigen-value theory to analyze its stability. Secondly, we discuss the existence of bionomic equilibrium. Finally we construct the Hamiltonian function and use the Pontryagin maximum principle to solve the optimal harvesting.