Several Types Of The Population Model With Stage Structure Of Research

People have been developing economy with simple and crude manner in the past years, and the natural environment and resource are destructed seriously. Therefore a variety of ecological problems appeared.It is a kind of retaliation to the human. In recent years, people have noticed some problems during the development process, and paid more and more attention to sustainable development. And in the biological natural resources development and management, people benefit in the economic simultaneously, and they also begin to attach importance to the ecological benefits. Recently, science research workers begin to interdisciplinary cooperation to study the problem of biological resources’ development and management. This paper mainly studied the species with stage structure and function of reaction, including the optimal receiving strategy problem of competition model and predator-prey model. The whole thesis is composed of five chapters:In the first chapter,we introduce the relating background knowledge and the corresponding research situation at home and abroad about a stage-structured the mathematical model with function of reaction,also give some preliminaries.In the second chapter,we study a stage-structure competition systemwith the optimal harvesting policy and cannibalism,by using Lyapunov function we get the positive equilibrium point of attracting global scope,at the same time,by using Pontryagin’s maximum principle, we analysed the problem of optimal taxation strategy and optimal solutions.In the third chapter we study a stage-structured predator-prey model with time delay and the ratio function of the reaction,The boundary equilibrium and stability of the positive equilibrium point are figured out by using the Hurwitz theorem, the successive iteration method and the comparison theorem of differential equations. And it also proves that the system sustains persistently under certain conditions.In the fourth chapter some properties of the model with tax are added on the basis of the model in the third chapter. And the corresponding conclusions are drawn by discussing time-delay’s existence,: ??0,Lyapunov function are used to get the positive equilibrium point of the system to attract global scope. Meanwhile,Pontryagin maximum principle is used to analyze the optimal harvesting strategy. and the final optimal solutions are obtained.??0,when the time delay0?? ?,system has experienced the Hopf branch.The fifth chapter is conclusion part, which make a summary of this thesis and point out this thesis’ s limitations and the problems that need to be studied in the future.