Dynamics Analysis Of A Toxin-mediated Size-structured Population Model

Environmental pollution has a significant impact on the extinction and persistence of the population.Considering that the different size of population has different sensitivities to toxin,it is necessary to establish a size-structured population model with toxin effect.Proving the existence and uniqueness of the solution is one of the main problems of researching population dynamics.Therefore,we analyze two models in this thesis.The theoretical and numerical results are presented in the first toxin-mediated size-structured population model.In the second model,we consider that a juveniles-adult age-sizestructured population model and that prove the existence and uniqueness of the solution of the model.This thesis mainly consists of four parts.In chapter 1,the background knowledge and existing research on toxin-mediated ordinary differential and delay differential population models,age-structured and sizestructured models are introduced,the study content of this thesis are presented,and some preliminaries are reviewed.In chapter 2,a size-structured model with toxin effect is established.The existence and uniqueness of solution of this model is proved by the following steps:(1)The model is transformed into an integral equations,the definitions of solution,upper and lower solutions are given.(2)The convergence of solution is proved by constructing monotone sequences.(3)The existence and uniqueness of solution is proved.By constructing upper and lower solutions,we discussed the following cases:(1)The conditions of persistence and extinction of population without toxin effect.(2)The conditions of persistence of population when the input rate and decay rate of toxin are constants.(3)The conditions of persistence and extinction of population when the limits of input rate and decay rate depending on time exist.Finally,the numerical simulation results are presented to verify the results,and the long-term dynamic behavior of the population is studied when the input rate of toxin is periodic.Chapter 3 proves that the existence and uniqueness of solution for nonautonomous continous age-size-structured model which describes the dynamics of a population composed of juveniles and adults population by using Banach fixed point theorem.The specific steps are as follows:(1)The model is transformed into an integral system.(2)Appropriate complete metric space and operator are constructed.(3)The existence and uniqueness of solution by using Banach fixed theorem is proved.In the last chapter,the main work of this paper is summarized briefly,and the main conclusions obtained in this paper are described,and some shortcomings in the article and future work are discussed.