The Optimal Harvesting Problems Of Two Classes Of Population Systems

Researches on the change of population in the rational utilization and protection of bio-logical resources and so on various aspects has a very important application value. However, population system models according to different realities can reflect the number of population changes from different aspects. For decades, many scholars at home and abroad dedicated to the study of the control problem of population system and obtained the rich research achieve-ments.The theoretical results are widely applied to real life. In the study of population system, the optimal harvesting problem has very important economic significance and practical signif-icance. Therefore, we considerate the optimal harvesting problem of two classes of population systems. According to the content, the total is divided into three parts as follows:The first chapter is an introduction, mainly introducing the background of selected topics and research status.The second chapter mainly studies the prey population systems depending on the optimal harvesting problem of the individual scale structure. Firstly, by using the method of charac-teristic line we can get the expression of the solution.Then.by using the fixed point theorem we can prove the existence and uniqueness of the solution. Last, by applying the method of conjugate system and cone knowledge we can obtain the optimality conditions of the optimal control problems.The third chapter discuss the optimal harvesting problem of population systems relating to age in polluted environment.In this chapter,we conclude the existence and uniqueness of the solution, the continuous dependence of the solution on the control variables and the optimality conditions of the optimal harvesting.