The Optimal Control Problem Of Competing Population Systems With Time Delay And Age-dependent

With the rapid development of economy and society, a variety of biological resources has suffered serious damage, which arouses people great attention on the living environment, there-fore research on biological population systems which are closely related with living environment have a great significance. By now, the control problems of population system with age distri-bution are studied in a large amount of literature, and lots of important results are achieved. While there are relatively rare studies on control problems with time delay and age-dependent. In this paper, it is mainly discussed the optimal control for competing population systems with time delay and age-dependent. According to the contents, it is divided into three chapters:In the first chapter, it introduces the background. the present study situation of population dynamics system at home and abroad and the preparative theories.In the second chapter, a class of non-linear population systems with time delay and age-dependent is discussed. By the fixed-point theorem and Gronwall lemma, the existence and uniqueness of their solution are proved.In the third chapter, an optimal control problem of competing population systems with time delay and age-dependent is researched. And the model of the conjugated system is con-structed, moreover the necessary condition of optimal control problem is obtained by means of the conception of normal cone.