• 论文 •

### 带有离散个体等级结构的种群系统的控制问题

1. 杭州电子科技大学运筹与控制研究所, 杭州 310018
• 出版日期:2020-03-25 发布日期:2020-05-30

HE Zerong,CHEN Huai,XIE Qiangjun. Control Problems of a Discrete Hierarchical Population System[J]. Journal of Systems Science and Mathematical Sciences, 2020, 40(3): 410-422.

### Control Problems of a Discrete Hierarchical Population System

HE Zerong ,CHEN Huai ,XIE Qiangjun

1. Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018
• Online:2020-03-25 Published:2020-05-30

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.

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