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"

1 ANITA S . Optimal harvesting for a nonlinear age-dependent population dynamics[J]. Journal of Mathematical Analysis and Applications, 1998, 226 (1): 6- 22.
doi: 10.1006/jmaa.1998.6064
2 倪冬冬. 年龄等级结构种群模型的适定性、算法与最优收获[D]. 杭州: 杭州电子科技大学, 2019.
NI Dongdong. Well-posedness, algorithm and optimal harvesting of a continuous hierarchical age-structured population model[D]. Hangzhou: Hangzhou Dianzi University, 2019.
3 何泽荣, 周楠. 具有年龄等级结构的种群竞争系统的最优收获控制[J]. 数学物理学报(A辑), 2022, 42 (1): 228- 244.
HE Zerong , ZHOU Nan . Optimal harvesting in a competing system of hierarchical age-structured populations[J]. Acta Mathematica Scientia (Series A), 2022, 42 (1): 228- 244.
4 CHEN Bin , SERGEY A T . Optimal control of a population dynamics model with hysteresis[J]. Acta Mathematica Scientia, 2022, 42 (1): 283- 298.
doi: 10.1007/s10473-022-0116-x
5 祁慧敏, 雒志学. 具有年龄结构的周期种群动力系统的最优控制[J]. 山东大学学报(理学版), 2023, 58 (5): 46- 52.
QI Huimin , LUO Zhixue . Optimal harvesting for periodic age-structured population dynamics[J]. Journal of Shandong University(Natural Science), 2023, 58 (5): 46- 52.
6 张海霞, 卢殿臣. 具有年龄结构的n种群竞争系统的最优收获[J]. 科学技术与工程, 2007, 7 (23): 5987- 5990.
doi: 10.3969/j.issn.1671-1815.2007.23.003
ZHANG Haixia , LU Dianchen . Optimal harvesting control problem for an age-dependent competing system of n species[J]. Science Technology and Engineering, 2007, 7 (23): 5987- 5990.
doi: 10.3969/j.issn.1671-1815.2007.23.003
7 徐春荣, 赵春. n种群非线性竞争系统的最优输入率控制[J]. 天津师范大学学报(自然科学版), 2010, 30 (3): 1- 6.
XUE Chunrong , ZHAO Chun . Optimal inputting rate control of n species nonlinear competing system[J]. Journal of Tianjin Normal University(Natural Science Edition), 2010, 30 (3): 1- 6.
8 ZHANG Tainian , LUO Zhixue , ZHANG Hao . Optimal harvesting for a periodic n-dimensional food chain model with size structure in a polluted environment[J]. Mathematical Biosciences and Engineering, 2022, 19 (8): 7481- 7503.
doi: 10.3934/mbe.2022352
9 HE Zerong . Optimal birth control of age-dependent competitive species[J]. Journal of Mathematical Analysis and Applications, 2004, 296 (1): 286- 301.
doi: 10.1016/j.jmaa.2004.04.052
10 HE Zerong , CHENG Jishu , ZHANG Chunguo . Optimal birth control of age-dependent competitive species Ⅲ overtaking problem[J]. Journal of Mathematical Analysis and Applications, 2008, 337 (1): 21- 35.
doi: 10.1016/j.jmaa.2007.03.082
11 LUO Zhixue . Optimal brith control for an age-dependent competition system of n species[J]. Science and Complexity, 2007, 20 (3): 403- 415.
doi: 10.1007/s11424-007-9036-z
12 LUO Zhixue , HE Zerong , LI Wantong . Optimal birth control for predator-prey system of three species with age-structure[J]. Applied Mathematics and Computation, 2004, 155 (3): 665- 685.
doi: 10.1016/S0096-3003(03)00808-7
13 雒志学, 杜明银. 一类具年龄结构n维食物链模型的最优收获控制[J]. 应用数学和力学, 2008, 29 (5): 618- 630.
LUO Zhixue , DU Mingyin . Optimal harvesting for an age-dependent n-dimensional food chain model[J]. Applied Mathematics and Mechanics, 2008, 29 (5): 618- 630.
14 HE Zerong . Optimal harvesting of two competing species with age dependence[J]. Nonlinear Analysis: Real World Applications, 2006, 7 (4): 769- 788.
doi: 10.1016/j.nonrwa.2005.04.005
15 ANITA S . Analysis and control of age-dependent population dynamics[M]. Dordrecht: Kluwer Academic Publishers, 2000.
16 付军, 朱宏. 具年龄和加权的半线性种群系统的最优边界控制[J]. 吉林大学学报(理学版), 2013, 51 (1): 27- 33.
FU Jun , ZHU Hong . Optimal boundary control for a semi-linear age-dependent population system based on weight[J]. Journal of Jilin University(Science Edition), 2013, 51 (1): 27- 33.
17 BARBU V , IANNELLI M . Optimal control of population dynamics[J]. Optim Theo Appl, 1999, 102 (1): 1- 14.
doi: 10.1023/A:1021865709529
[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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