年龄等级结构两种群系统模型分析与最优控制  

Model Analysis and Optimal Control in a Hierarchical Two Age-Structured Population System

作　　者：祁慧敏 雒志学[1] QI Huimin;LUO Zhixue(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《系统科学与数学》2023年第3期559-576,共18页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11561041);甘肃省自然科学基金(1506RJZA071)资助课题。

摘　　要：文章提出一类带有年龄等级结构的两种群竞争系统模型,主要研究模型的适定性和最优控制问题.首先,通过冻结系数法和特征线法以及不动点定理推出解的存在唯一性,并说明了解的非负有界性;其次,运用积分不等式得出了解对控制变量的连续性结果;最后,利用切锥法锥与共轭系统导出了最优性条件,运用Ekeland变分原理及不动点定理证明了最优控制的存在唯一性,为两种群控制问题及模型的应用提供了科学依据.This paper is concerned with model analysis and optimal control in a hierarchical two age-structured population system.First and foremost,the existence,uniqueness,nonnegativity and boundedness of solutions to the model are established by freezing coeficient method,characteristic line method and fixed point theorem.Next,we obtain that the population density depends continuously on the control variable through integral inequalities.Last but not least,the optimality conditions are derived by means of tangent-normal cones and adjoint system.Futhermore,the existence and uniqueness of the optimal control are demonstrated via Ekeland variational principle and fixed point theorem,which provided scientific basis for control problems and model applications.

关 键 词：年龄等级结构 不动点 变分原理 法锥 

分 类 号：O175[理学—数学]