具有Size结构的捕食种群系统的最优收获策略

数学物理学报 ›› 2012, Vol. 32 ›› Issue (1): 90-102.

具有Size结构的捕食种群系统的最优收获策略

刘炎¹, 何泽荣²

1.浙江大学数学系杭州 310027|2.杭州电子科技大学运筹与控制研究所杭州 310018

收稿日期:2010-10-22 修回日期:2011-12-17 出版日期:2012-02-25 发布日期:2012-02-25
基金资助:
国家自然科学基金 (10871179, 11061017)资助

Optimal Harvesting of a Size-structured Predator-prey Model

LIU Yan¹, HE Ze-Rong²

1.Department of Mathematics, Zhejiang University, Hangzhou 310027;
2.Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018

Received:2010-10-22 Revised:2011-12-17 Online:2012-02-25 Published:2012-02-25
Supported by:
国家自然科学基金 (10871179, 11061017)资助

摘要/Abstract

摘要：

分析了一类捕食者种群带有Size结构的捕食-被捕食系统的最优收获问题. 利用不动点定理证明了状态系统及其共轭系统非负解的存在唯一性、解对控制变量的连续依赖性. 应用切锥法锥技巧导出了最优性条件, 借助Ekeland变分原理讨论了最优收获策略的存在唯一性, 推广了年龄结构种群模型中的相应结论.

关键词: 最优控制, 捕食-被捕食模型, Size结构, 切锥法锥, Ekeland变分原理

Abstract:

This work is concerned with an optimal harvesting problem for a predator-prey model, in which the prey population is described by a first order partial differential equation (PDE) in a density function and the predator by an ordinary di?erential equation in total size. The existence and uniqueness of solutions to the state system and the dual system is proven via fixed point theorem. Necessary optimality conditions of first order are established by use of tangent-normal cones and dual system technique. The existence of a unique optimal control
pair is derived by means of Ekeland’s variational principle. The resulting conclusion extends some existing results involving age-dependent populations.

Key words: Optimal control, Predator-prey model, Size-structure, Tangent-normal cones, Ekeland’s variational principle

中图分类号:

92B05

刘炎, 何泽荣. 具有Size结构的捕食种群系统的最优收获策略[J]. 数学物理学报, 2012, 32(1): 90-102.

LIU Yan, HE Ze-Rong. Optimal Harvesting of a Size-structured Predator-prey Model[J]. Acta mathematica scientia,Series A, 2012, 32(1): 90-102.

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