Well-posedness,Algorithm And Optimal Harvesting Of A Continuous Hierarchical Age-structured Population Model

The difference of dominance rank of individuals within a biological population is widely observed.As far as current progresses in relative field are concerned,the research results on the population system based on hierarchy structure are fewer than age-/sizestructured systems,and works on control problems of this kind of models can be rarely seen.This dissertation is concerned with a hierarchical age-structured population model,which is a partial integro-differential equation with a global feedback boundary condition.We study dynamical properties of this model;investigate two kinds of optimal harvesting problems for the system;and some numerical results are presented beside the theoretic analyses.The research results are included in chapters 2 and 3.The second chapter focuses on system analysis.Section 1 presents the model description and some assumptions.In section 2,we study the well-posedness of the model,the existence and uniqueness of solutions of this system are proved by fixed-point theorem.In addition,we show that the solution is non-negative and continuous with respect to the initial age distribution.In section 3,we prove the existence of positive equilibria and discuss the stability of zero steady state.In section 4,we propose a numerical method for solving the model and show its convergence.In addition,we show some numerical results.The third chapter is devoted to two optimal harvesting problems of the hierarchical age-structured system.Section 1 gives a brief description of the problem.In section 2,we discuss an optimal harvesting problem which maximizes the benefits.We prove the existence of optimal controls and obtain the maximum principle.In section 3,we investigate a minimization problem,the aim is to minimize the deviation between the final state and a prescribed distribution and the control costs.We establish the existence and uniqueness of the optimal control and derive the optimal feedback control law.In sections 2 and 3,several relevant numerical results are also contained.