一类非线性年龄等级结构种群系统模型的可控性  

Controllability of a hierarchical age-structured population system model

作　　者：何泽荣[1] 周楠 韩梦杰 HE Ze-rong;ZHOU Nan;HAN Meng-jie(Institute of Operational Research and Cybernetics,Hangzhou Dianzi University,Hangzhou 310018,China)

机构地区：[1]杭州电子科技大学运筹与控制研究所,浙江杭州310018

出　　处：《高校应用数学学报（A辑）》2020年第2期191-198,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

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

摘　　要：研究一类基于年龄等级差异的种群系统的近似可控性问题,状态方程由非线性偏微分-积分方程描述,且边界条件具有全局反馈特征.运用冻结系数法、线性系统可控性和集值映射不动点原理确立了系统可控性,表明了种群状态可通过个体迁移调节.The controllability of a class of hierarchical age-structured population system is studied,in which the state equation is described by a nonlinear partial integro-differential equation with a boundary condition of global feedback.The approximate controllability of the system is established by means of frozen coefficients,a result for linear system and the Kakutani fixed point theorem of multi-valued mappings.The conclusion shows that the population state can be adjusted by individuals migration process.

关 键 词：年龄等级 种群模型 偏微分-积分方程 近似可控性 Kakutani不动点 

分 类 号：O231.2[理学—运筹学与控制论] O175.6[理学—数学]