基于尺度结构的周期三种群系统的最优收获

doi:10.6040/j.issn.1671-9352.0.2021.355

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (1): 77-88.doi: 10.6040/j.issn.1671-9352.0.2021.355

• • 上一篇

基于尺度结构的周期三种群系统的最优收获

张昊,雒志学,郑秀娟

兰州交通大学数理学院, 甘肃兰州 730070

发布日期:2021-12-21
作者简介:张昊(1997— ),女,硕士研究生,研究方向为生物数学及最优控制理论. E-mail:zhanghao20210709@163.com
基金资助:
国家自然科学基金资助项目(11561041)

Optimal harvesting for three species system with size-structures in periodic environments

ZHANG Hao, LUO Zhi-xue, ZHENG Xiu-juan

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

Published:2021-12-21

摘要/Abstract

摘要： 在周期环境下研究依赖尺度结构的三维食物链模型的最优收获问题。首先,运用Banach不动点定理推导出系统非负有界解的存在唯一性,其次运用切锥-法锥概念得出最优控制问题的解为最优的必要条件,最后,通过Ekeland变分原理,证明最优控制的存在唯一性。

关键词: 最优收获, 周期环境, 尺度结构, Ekeland变分原理

Abstract: The paper investigates the optimal harvesting for three-dimensional food chain model with size-structures in periodic environments. Firstly, by applying the theorem of Banach fixed point, we establish the existence and uniqueness of nonnegative bounded solutions. Secondly, we obtain the necessary conditions by using the tangent-normal cones. Finally, on the basis of Ekelands variational principle, we conclude that a unique optimal policy exists.

Key words: optimal harvesting, periodic environment, size-structure, Ekelands variational principle

中图分类号:

O175.1

张昊,雒志学,郑秀娟. 基于尺度结构的周期三种群系统的最优收获[J]. 《山东大学学报(理学版)》, 2022, 57(1): 77-88.

ZHANG Hao, LUO Zhi-xue, ZHENG Xiu-juan. Optimal harvesting for three species system with size-structures in periodic environments[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(1): 77-88.

参考文献

[1] ANITA S. Analysis and control of age-dependent population dynamics[M]. Dordrecht: Kluwer Academic Publishers, 2000: 65-103.
[2] 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, 25A(6): 905-912. LUO Zhixue, WANG Miansen. Optimal harvesting control problem for linear periodic age-dependent population dynamic system[J]. Acta Mathematica Scientia, 2005, 25A(6):905-912.
[3] LUO Zhixue. Optimal control for a predator-prey system with age-dependent[J]. International Journal of Biomathematics, 2009, 2(1):45-59.
[4] LUO Zhixue, DU Mingyin. Optimal harvesting for an age-dependent n-dimensional food chain model[J]. Applied Mathematics and Mechanics(English Edition), 2008, 29(5):683-695.
[5] WERNER E E, GGILLIAM J F. The ontogenetic niche and species interactions in size-structured populations[J]. Annual Review of Ecology Evolution and Systematics, 1984, 15:393-425.
[6] 刘荣,何泽荣,刘丽丽. 周期环境中尺度结构线性种群模型的适定性[J]. 杭州电子科技大学学报, 2013, 33(1):80-83. LIU Rong, HE Zerong, LIU Lili. Well-posedness of a linear size-structured population model in periodic environments[J]. Journal of Hangzhou Dianzi University, 2013, 33(1):80-83.
[7] 何泽荣,刘荣,刘丽丽. 周期环境中基于个体尺度的种群模型的最优收获策略[J]. 应用数学学报, 2014, 37(1):145-159. HE Zerong, LIU Rong, LIU Lili. Optimal harvesting of a size-structured population model in a periodic environment[J]. Acta Mathematicae Applicatae Sinica, 2014, 37(1):145-159.
[8] LIU Yan, CHENG Xiaoliang, HE Zerong. On the optimal harvesting of size-structured population dynamics[J]. Applied Mathematics: A Journal of Chinese Universities, 2013, 28(2):173-186.
[9] 冯变英,李秋英. 一类基于个体尺度的种群模型的适定性及最优不育控制策略[J]. 系统科学与数学, 2016, 36(2):278-288. FENG Bianying, LI Qiuying. Optimal contraception control for a size-structured population model[J]. Journal of Systems Science and Mathematical Sciences, 2016, 36(2):278-288.
[10] LIU Rong, LIU Guirong. Maximum principle for a nonlinear size-structured model of fish and fry management[J]. Nonlinear Analysis: Modelling and Control, 2018, 23(4):533-552.
[11] 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, 32A(1):90-102. LIU Yan, HE Zerong. Optimal harvesting of a size-structured predator-prey model[J]. Acta Mathematica Scientia, 2012, 32A(1):90-102.
[12] ZHANG Fengqian, LIU Rong, CHEN Yuming. Optimal harvesting in a periodic food chain model with size structures in predators[J]. Applied Mathematics & Optimization, 2017, 75(2):229-251.
[13] 梁丽宇, 雒志学. 周期环境中具有尺度结构的两种群系统的最优控制[J]. 山东大学学报(理学版), 2019, 54(9):69-75. LIANG Liyu, LUO Zhixue. Optimal control of a size-structured system with two species in periodic environments[J]. Journal of Shandong University(Natural Science), 2019, 54(9):69-75.

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基于尺度结构的周期三种群系统的最优收获

Optimal harvesting for three species system with size-structures in periodic environments

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