具有年龄结构的线性周期种群动力系统的最优收获控制问题

数学物理学报 ›› 2005, Vol. 25 ›› Issue (6): 905-912.

具有年龄结构的线性周期种群动力系统的最优收获控制问题

雒志学, 王绵森

兰州交通大学数学系兰州 730070 西安交通大学数学系西安 |710049

出版日期:2005-12-24 发布日期:2005-12-24
基金资助:
兰州交通大学‘青蓝’人才工程基金(QL0518A)、国家自然科学基金(604730 304)资助

Optimal Harvesting Control Problem for Linear Periodic Age dependent Population Dynamic System

LUO Zhi-Hua, WANG Mian-Sen

Online:2005-12-24 Published:2005-12-24
Supported by:
兰州交通大学‘青蓝’人才工程基金(QL0518A)、国家自然科学基金(604730 304)资助

摘要/Abstract

摘要：

研究一类具有年龄结构的线性周期种群动力系统的最优收获控制问题,即讨论了具有周期的生死率和周期变化的收获项的Lotka Mckendrick模型.利用Mazur's定理,作者证明了控制问题最优解的存在性,同时借助于法锥概念,还得到了控制问题最优解存在的必要条件。最后，在适当的假设下，得到了最优控制问题的唯一解。该文的结论推广了某些已有的结果. 

关键词: 最优收获;最优控制;周期种群动力学;最大值原理

Abstract:

In this paper, an optimal harvesting problem for linear periodic age\|dependent population dynamics is investigated. Namely, the Lotka\|Mckendrick model with periodic vital rates and a periodic forcing term that sustains oscillations is considered. By Mazur's theorem, existence of solutions of the optimal control problem is demonstrated and by the conception of normal cone, first order necessary conditions of optimality for the problem are
obtained. Finally, under suitable assumptions, uniqueness of solution of the optimal control problem is given. The results extend some known criteria.

Key words: Optimal harvesting, Optimal , control, Periodic popu lation dynamics, The maximum principle

中图分类号:

35B10

雒志学, 王绵森. 具有年龄结构的线性周期种群动力系统的最优收获控制问题[J]. 数学物理学报, 2005, 25(6): 905-912.

LUO Zhi-Hua, WANG Mian-Sen. Optimal Harvesting Control Problem for Linear Periodic Age dependent Population Dynamic System [J]. Acta mathematica scientia,Series A, 2005, 25(6): 905-912.

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