具有年龄等级结构的种群竞争系统的最优收获控制

摘要/Abstract

摘要：

该文研究一类带有年龄等级结构的种群竞争模型的最优收获强度控制问题.证明了最优策略的存在性，关于含有分布式和边界控制函数的偏微分积分系统建立了一个新的连续性定理，据此并运用法锥和共轭系统技巧对最优策略进行了精确刻画.此外，也展示了一些数值实验结果，考察了价格函数对最优收益的影响.

关键词: 年龄等级, 竞争系统, 最优控制, 法锥, 预紧性

Abstract:

In this paper, we investigate an optimal control problem for a hierarchical system of age-dependent competing populations, with the removal intensity as the control variable. After the existence of optimal strategies has been established, we prove a new continuity result, by which the optimal policies are exactly characterized with a normal cone and an adjoint system. Furthermore, some numerical results are presented to show the effects of the price on optimal profits.

Key words: Hierarchy of age, Competing system, Optimal control, Normal cone, Pre-compactness

中图分类号:

O211.4

何泽荣,周楠. 具有年龄等级结构的种群竞争系统的最优收获控制[J]. 数学物理学报, 2022, 42(1): 228-244.

Zerong He,Nan Zhou. Optimal Harvesting in a Competing System of Hierarchical Age-Structured Populations[J]. Acta mathematica scientia,Series A, 2022, 42(1): 228-244.

图/表 9

图 1

最优控制 $u_1^{*}(a, t)$ 与 $u_2^{*}(a, t)$ ( $s=0)$ "

图 1

图 2

最优密度 $p_1^{*}(a, t)$ 与 $p_2^{*}(a, t)$ ( $s=0)$ "

图 2

图 3

最优控制 $u_1^{*}(a, t)$ 与 $u_2^{*}(a, t)$ ( $s=1)$ "

图 3

图 4

最优密度 $p_1^{*}(a, t)$ 与 $p_2^{*}(a, t)$ ( $s=1)$ "

图 4

图 5

最优控制 $u_1^{*}(a, t)$ 与 $u_2^{*}(a, t)$ ( $s=2)$ "

图 5

图 6

最优密度 $p_1^{*}(a, t)$ and $p_2^{*}(a, t)$ ( $s=2)$ "

图 6

图 7

最优控制 $u_1^{*}(a, t)$ 与 $u_2^{*}(a, t)$ ( $s=3)$ "

图 7

图 8

最优密度 $p_1^{*}(a, t)$ 与 $p_2^{*}(a, t)$ ( $s=3)$ "

图 8

表 1

参考文献 33

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