非线性年龄等级结构种群系统的近似能控性  

Approximate Controllability for a Nonlinear Hierarchical Age-Structured Population System

作　　者：何泽荣[1] 王淑平 章春国 HE Zerong;WANG Shuping;ZHANG Chunguo(Institute of Operational Research and Cybernetics,Hangzhou Dianzi University,Hangzhou 310018)

机构地区：[1]杭州电子科技大学运筹与控制研究所,杭州310018

出　　处：《系统科学与数学》2020年第5期775-782,共8页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11871185);浙江省自然科学基金(LY18A010010)资助课题。

摘　　要：研究一类基于年龄的等级结构种群模型的近似能控性,状态系统由具有全局反馈边界条件的非线性偏微分-积分方程描述,控制手段为迁移(投放或移除).以线性系统的能控性为基础,借助冻结系数法和集值映射的Ky Fan-Glicksberg不动点定理,确立了非线性系统的近似能控性.This paper is concerned with approximate controllability of a nonlinear hierarchical age-structured population model.Based upon the core assumption that the mortality and fertility of an individual of age a depend more on the number of individuals with age older than a,the state system is described by an integropartial differential equation with a globally feedback boundary condition,and the control policy stands for the migration process(inflow or emigration).For the strongly nonlinear population system,the distributed approximate controllability is established by combining frozen coefficients and the Ky Fan-Glicksberg fixed point theorem of set-valued maps with a controllability result of a linear system in the literature.

关 键 词：个体等级 种群模型 能控性 集值映射 不动点定理 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]