提出一类基于离散个体等级结构的非线性种群模型, 研究它的 相关控制问题, 包括系统可控性、镇定与最优收获问题. 证明了系统的上~(下)~可 控性、精确可控性和镇定性. 仔细刻画了最优收获策略, 对三类情形给出了具体的 收获强度公式. 通过数值模拟分析了个体经济价值对最优策略的影响.

This paper proposes a class of hierarchical population model, in form of nonlinear system of difference equations, and studies several control problems, including controllability, stabilization and optimal harvesting. The upper and lower controllability are proven by a corresponding result of suitable linear systems and the comparison principle, and the associated control strategies are constructed. On the other hand, the exact controllability of the population system is established by means of frozen coefficients, linear controllability and the Kakutani fixed point theorem of set-valued maps. The stabilization result follows from the linearization around zero solution and its controllability. Furthermore, a kind of optimal harvesting problems are investigated. General policy is carefully described and, in three special cases, concrete results are obtained. Finally, the effects of individuals economic values on harvesting efforts are examined by a numerical approach.