The Optimal Control Problem Of Two Classes Of Population Systems Based On Hierarchical Structure

The hierarchical structure of the population includes age,scale and aggressiveness,which have important effects on the dynamic parameters of population development(fertility rate,mortality rate,etc.),such as the relatively low fertility rate of older individuals,and the mortality rate is high.Considering these hierarchical differences in establishing the population model can make the modeling result more close to the actual situation and reflect the development law of the population more accurately.Therefore,it is of great theoretical and practical significance to study the optimal control of hierarchical population systems.In this article,we mainly study the optimal control problem of two classes of population systems based on hierarchical structure.In the first chapter,the historical development and research status of the optimal control of population system are briefly introduced.In the second chapter,The optimal control of a class of population system with hierarchical structure is studied.Firstly,the existence and uniqueness of the solution of the system model is proved by the fixed point theory;secondly,the continuous dependence of the solution on the control variable is investigated,and the necessary condition of optimal control is obtained by means of the Tangent cone-normal theory.In the third chapter,The optimal control problem of a class of competitive population system based on hierarchical structure is discussed.Firstly,the existence and uniqueness of the solution of the population system can be validated by the Fixed-point Theorem.Secondly,the continuous dependence of the solution on the control variable is discussed,and the necessary condition of the optimal control is established by the property of the conjugate system and the Tangent cone-normal theory.