JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (10): 75-83.doi: 10.6040/j.issn.1671-9352.0.2023.207

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Optimal birth control of n species nonlinear competition system with age-structure

Zijuan ZHOU(),Zhixue LUO*()   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2023-05-08 Online:2023-10-20 Published:2023-10-17
  • Contact: Zhixue LUO E-mail:717567249@qq.com;luozhixue2009@126.com

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Abstract:

The optimal birth control of n species nonlinear competition system with age-structure is investigated. The existence and uniqueness of non-negative solution of the system is proved by using the fixed-point theorem. The extremization sequence is constructed, and Mazur?s theorem are used to verify the existence of the optimal solution of the optimal birth control problem, and the necessity conditions are derived out via normal cone and conjugate system techniques.

Key words: age-structure, competitive population, optimal birth control, adjoint system, normal cone

CLC Number: 

  • O175.1

Fig.1

Individual distribution density of the population Ⅰ and Ⅱ"

Fig.2

Total scale of the population Ⅰ andⅡ"

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[1] QI Huimin, LUO Zhixue. Optimal harvesting for periodic age-structured population dynamics [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(5): 46-52.
[2] XU Yang, ZHAO Chun. Optimal control of competitive population system with hierarchical structure [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(11): 61-70.
[3] ZHENG Xiu-juan, LUO Zhi-xue, ZHANG Hao. Optimal control of nonlinear competing populations based on the size-structure [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(11): 51-60.
[4] 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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[6] CHENG Hui-dong, CHANG Zheng-bo. Continuous harvesting on the predator mathematical model  with impulsive stocking and stage-structured [J]. J4, 2010, 45(11): 83-87.
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