JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (5): 46-52.doi: 10.6040/j.issn.1671-9352.0.2022.435

Previous Articles    

Optimal harvesting for periodic age-structured population dynamics

QI Huimin, LUO Zhixue*   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2023-05-15

Abstract: An optimal harvesting problem for periodic age-structured population dynamics is analyzed. Using the Mazur theorem and corollary, the existence of the optimal solution is proved. In addition the optimality conditions are derived by the adjoint system and normal cone.

Key words: age-structured, periodic population, optimal control, normal cone

CLC Number: 

  • O175.1
[1] CLARK C W. Mathematical bioeconomics: the optimal management of renewable resources[M]. 2nd. New York: John Wiley and Sons Inc, 1990.
[2] ANITA S. Optimal harvesting for a nonlinear age-dependent population dynamics[J]. Journal of Mathematical Analysis and Applications, 1998, 226(1):6-22.
[3] ANITA S, IANNELLI M, KIM E J, et al. Optimal harvesting for periodic age-dependent population dynamics[J]. SIAM J Appl Math, 1998, 58(5):1648-1666.
[4] 何泽荣.具有年龄结构的捕食种群系统的最优收获策略[J].系统科学与数学, 2006, 26(4):467-483. HE Zerong. Optimal harvesting for an age-structured predator-prey system[J]. Journal of Systems Science and Mathematical Sciences, 2006, 26(4):467-483.
[5] SUN H Y, ZHAO C. The well posedness and the optimal control of two competing species with age dependence[J]. Acta Mathematica Applicatae Sinica, 2010, 33(6):1037-1048.
[6] 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 Zhixue. Optimal birth rate control for competing populations dependent on scale structure[J]. Journal of Shandong University(Natural Science), 2020, 55(11):18-25.
[7] 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, 2022, 42A(1):228-244. HE Zerong, ZHOU Nan. Optimal harvesting in a competing system of hierarchical age-structured populations[J]. Acta Mathematica Scientia, 2022, 42A(1):228-244.
[8] BARBU V. Mathematical methods in optimization of differential systems[M]. London: Kluwer Academic Publishers, 1994.
[9] ANITA S. Analysis and control of age-dependent population dynamics[M]. Dordrecht: Kluwer Academic Publishers, 2000.
[10] 程其襄,张奠宙,胡善文,等.实变函数与泛函分析基础[M]. 北京:高等教育出版社, 2019. CHENG Qixiang, ZHANG Dianzhou, HU Shanwen, et al. Real variable function and fundamental of functional analysis[M]. Beijing: Higher Education Press, 2019.
[11] BARBU V, PRECUPANU T. Convexity and optimization in banach spaces[M]. London: D Reidel Publishing Company, 1986.
[1] DU Fang-fang, SUN Tong-jun. Cubic B-spline finite element method for parabolic optimal control problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(4): 40-48.
[2] LI Na, LUO Zhi-xue. Optimal control for competing species with diffusion and size-structure [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(1): 69-76.
[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] 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.
[5] YANG Cai-jie, SUN Tong-jun. Crank-Nicolson finite difference method for parabolic optimal control problem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(6): 115-121.
[6] ZHENG Rui-rui, SUN Tong-jun. A priori error estimates of finite element methods for an optimal control problem governed by a one-prey and one-predator model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(1): 23-32.
[7] LIANG Li-yu, LUO Zhi-xue. 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.
[8] CAO Xue-jing, LUO Zhi-xue. Optimal control of forest evolution system in polluted environment [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(7): 15-20.
[9] ZHANG Tai-nian, LI Zhao-xing. Convergence analysis for inverse problems in a degenerate parabolic equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 35-42.
[10] NIE Tian-yang, SHI Jing-tao. The connection between DPP and MP for the fully coupled forward-backward stochastic control systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(5): 121-129.
[11] LIU Jiang-bi, LUO Zhi-xue. Optimal control for a nonlinear diffusion system with age-dependent [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(5): 136-142.
[12] CAI Chao. An inverse problem of identifying the coefficient in a Kolmogorov type equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 127-134.
[13] YU Yong-sheng, GONG Zhao-hua, LIU Chong-yang. Optimal control problem in the microbial fed-batch fermentation process [J]. J4, 2011, 46(11): 117-121.
[14] ZHANG Huan-shui1, SONG Xin-min1, XIE Li-hua2. Stage-by-Stage optimization approach to optimal control for general timedelay systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2011, 46(10): 45-56.
[15] CHEN Li. Properties on Z for anticipated BSDE and application  in stochastic  control with delay [J]. J4, 2010, 45(4): 16-20.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!