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# The Optimal Control Problem of Two Size-structured Population Models

Author: ZhangHui
Tutor: ZhaoChun
School: Tianjin Normal University
Course: Applied Mathematics
Keywords: size-structured stationary solution the stability the optimal coutrol
CLC: O175
Type: Master's thesis
Year: 2013
Downloads: 4
Quote: 0
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### Abstract

 The optimal control of population system is a theorv which is closely related with the ecological balance.the biological diversification and the exploitation of renewable resources.By now,a lot of scholars have studied the control of age-structured population.and they have had a. lot of important results.In the same time.studying of Size-structured population is increasing popular.Size means a set of continuous indexes to target individuals.such as length.volume and so on.The applicability of Size-structured is better than the applicability of age-structured.This paper considers the optimal control problem of two Size-structured population models.This pa-per considers the optimal control problem of two Size-structured population models According to the contents.it is divided into three chapters:In the first chapter, it introduces the background.the present study situation and tin. preparative theories.In the second chapter.the stability conditions lor the stationarv solutien of a two-specie competitive size-structured population model is considered.The existence and uniqueness of the stationary solution arc proved by means ot fixed point theorem.The characteristic equation for the stationary solution is established by the knowledge of the ordinary diffeieutial equation.In the third chapter, the optimal control problem for inputting rate of a size-structured population model is studied.By the Banach fixed-point theorem.the existence and uniqueness of the solution are proved.The continuous dependence of the solution on control variable is given by using characteristic method.The necessary condition of optimality is derived by using the conception of normal cone and adjoint system

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