依赖尺度结构的竞争种群的最优出生率控制

doi:10.6040/j.issn.1671-9352.0.2020.320

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (11): 18-25.doi: 10.6040/j.issn.1671-9352.0.2020.320

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依赖尺度结构的竞争种群的最优出生率控制

张萍,雒志学^*

兰州交通大学数理学院, 甘肃兰州 730070

发布日期:2020-11-17
作者简介:张萍(1996— ),女,硕士研究生,研究方向为生物数学及最优控制理论. E-mail:1361049574@qq.com*通信作者简介:雒志学(1963— ),男,博士,教授,博士生导师,研究方向为生物数学及最优控制理论. E-mail:luozhix@263.net
基金资助:
国家自然科学基金资助项目(11561041);甘肃省自然科学基金资助项目(1506RJZA071)

Optimal birth rate control for competing populations dependent on scale structure

ZHANG Ping, LUO Zhi-xue^*

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

Published:2020-11-17

摘要/Abstract

摘要： 讨论了一个具有尺度结构的竞争种群模型。首先利用特征线法以及Banach不动点定理对系统解的存在惟一性予以证明,通过比较原理证明系统解对控制变量的连续依赖性;最后利用法锥的定义,证明最优控制存在的必要性。

关键词: 尺度结构, 出生率控制, 最优性条件, 竞争种群

Abstract: A competitive population model with scale structure-dependent is established, and the optimal birth-control problem of the model is discussed. Firstly, the existence and uniqueness of the system solution are proved by using the characteristic line method and the Banach fixed point theorem, and the continuous dependence of the system solution on the control variables is also proved by the comparison principle. At the end of the paper, the necessity condition of the existence of optimal control is proved by using the definition of normal cone.

Key words: scale structure, birth rate control, optimal condition, competitive population

中图分类号:

O715.1

张萍,雒志学. 依赖尺度结构的竞争种群的最优出生率控制[J]. 《山东大学学报(理学版)》, 2020, 55(11): 18-25.

ZHANG Ping, LUO Zhi-xue. Optimal birth rate control for competing populations dependent on scale structure[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(11): 18-25.

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依赖尺度结构的竞争种群的最优出生率控制

Optimal birth rate control for competing populations dependent on scale structure

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