Several Kinds Of Optimal Control Of Periodic Population Systems With Age-structure And Weighted Total Scale

Nowadays,human's living environment is getting worse and worse with the vigorous exploitation of natural resources.Nature's frequent disasters remind us of the importance of human conservation of biological diversity and optimal control of the ecological environment.The rich theory and advanced methods of cybernetics provide important value for the development and optimal control of populations.This paper studies the optimal control problems of several kinds of periodic population systems with age structure and weighted total scale.The survival rate of the population depends on the individual age and the weighted total scale.This paper is divided into four chapters according to the content:The first chapter is the introduction which mainly illuminates the background and significance of the selected topic,research status and existing problems.The second chapter is the preparation knowledge,which is mainly the lemma and theorems that need to be used in the proof process of this article.In the third chapter,based on the nonlinear population model,a mathematical model is established by taking into account the effects of population survival in the circulatory environment of change and the individual population age and the weighted total scale.Firstly,the characteristic line method is used to solve the formal solution of the model.Then,the knowledge of the existence and uniqueness of the learning is proved by the use of Bellman's lemma,Gronwall's Lemma and Banach's fixed point theorem.Finally,based on Mazur's theorem,the theory of cones and conjugate systems proves the existence of the optimal solution and its necessary conditions.The fourth chapter studies the competitive population model in the multi-population model.A mathematical model is established by taking into account the impact of population survival in the cyclical environment of change and the individual population age and the weighted total scale.The system's well-posedness,the existence of optimal solution and its necessary conditions are successively proved by using the feature line method,Bellman's Lemma,Gronwall's Lemma,Banach's fixed point theorem,Mazur's theorem,the cone and the conjugate system,and other knowledge.