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 integro-partial 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.