JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (1): 69-76.doi: 10.6040/j.issn.1671-9352.0.2021.223

Previous Articles    

Optimal control for competing species with diffusion and size-structure

LI Na, LUO Zhi-xue*   

  1. School of Mathematics and Physis, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2021-12-21

Abstract: The optimal control of a competitive population system with diffusion and size-structure is studied. Firstly, the existence and uniqueness of non-negative solution are obtained by comparison principle and the fixed point theorem. Secondly, Mazur theorem is used to prove the existence of optimal control. Finally, the optimality conditions are given by means of the normal cone definition and an adjoint system.

Key words: diffusion, size-structure, optimal control, competition

CLC Number: 

  • O175.1
[1] ANITA S. Analysis and control of age-dependent population dynamics[M]. Dordrecht: Kluwer Academic Publishers, 2000.
[2] 雒志学,李沐春. 具有扩散和年龄结构种群动力系统的最优控制[J]. 工程数学学报, 2006, 23(4):641-646. LUO Zhixue, LI Muchun. Optimal control for linear population dynamics with age-dependence spatial structure and diffusion[J]. Chinese Journal of Engineering Mathematics, 2006, 23(4):641-646.
[3] ZHAO Chun, WANG Miansen, ZHAO Ping. Optimal harvesting problems for age-dependent interacting species with diffusion[J]. Applied Mathematics and Computation, 2005, 163(1):117-129.
[4] 吴秀兰,付军.具有年龄结构和空间扩散的捕食与被捕食种群系统的最优控制[J]. 吉林大学学报(理学版), 2010, 48(4):545-550. WU Xiulan, FU Jun. Optimal control for age-dependent predator-prey population dynamics with diffusion[J]. Journal of Jilin University(Science Edition), 2010, 48(4):545-550.
[5] 刘江壁,雒志学.具有年龄结构非线性扩散系统的最优控制[J]. 山东大学学报(理学版), 2016, 51(5):136-142. LIU Jiangbi, LUO Zhixue. Optimal control for a nonlinear diffusion system with age-dependent[J]. Journal of Shangdong University(Natural Science), 2016, 51(5):136-142.
[6] 申柳肖,赵春. 基于尺度结构的竞争种群系统的最优输入率控制[J]. 山东大学学报(理学版), 2018, 53(7):21-29. SHEN Liuxiao, ZHAO Chun. Optimal control for inputting rate of a size-structure competitive system[J]. Journal of Shangdong University(Natural Science), 2018, 53(7):21-29.
[7] 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.
[8] 梁丽宇,雒志学. 基于尺度结构的捕食-食饵种群系统的最优收获率[J]. 系统科学与数学, 2019, 39(5):823-830. LIANG Liyu, LUO Zhixue. The optimal harvest rate for a predator-prey system with size-structure[J]. Journal of Systems Science and Mathematical Sciences, 2019, 39(5):823-830.
[9] 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.
[10] 刘炎,何泽荣. 一类基于尺度结构的种群系统的最优收获[J]. 系统科学与数学, 2015, 35(4):459-471. LIU Yan, HE Zerong. Optimal harvesting for a population system with body size[J]. Journal of Systems Science and Mathematical Sciences, 2015, 35(4):459-471.
[11] 章颖,何泽荣. 尺度结构竞争系统模型的最优收获策略[J]. 杭州电子科技大学学报, 2012, 32(6):198-200. ZHANG Ying, HE Zerong. Optimal harvesting strategy of a size-structured competitive system model[J]. Journal of Hangzhou Dianzi University, 2012, 32(6):198-200.
[12] BOUCEKKINE R, HRITONENKO N, YATSENKO Y. Optimal control of age-structured populations in economy, demograph, and the environment[M]. London: Routledge Taylor & Francis Group, 2011.
[13] BARBU V, IANNELLI M. Optimal control of population dynamics[J]. Journal of Optimization Theory & Applications, 1999, 102(1):1-14.
[1] ZHANG Bei-bei, XU Yao, ZHOU You, LING Zhi. Properties of the species invasion model with Allee effect [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(1): 50-55.
[2] LI You-ling, WANG Xuan. Attractors for the non-autonomous nonclassical diffusion equation with fading memory [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(9): 66-80.
[3] ZHOU Yan, ZHANG Cun-hua. Stability and Turing instability of a predator-prey reaction-diffusion system with schooling behavior [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(7): 73-81.
[4] QI Bin, CHENG Hao. Identification of source term for fractional diffusion-wave equation with Neumann boundary conditions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(6): 64-73.
[5] 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.
[6] 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.
[7] 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.
[8] PENG Bo, GUO Jing-jun. Asset pricing and simulation under the environment of jumping and mixed Gaussian process [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 105-113.
[9] 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.
[10] 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.
[11] HU Yong-liang, LUO Zhi-xue, LIANG Li-yu, FENG Yu-xing. Analysis of a stochastic single population system with age-dependent and diffusion in a polluted environment [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(9): 62-68.
[12] SHEN Liu-xiao, ZHAO Chun. Optimal control for inputting rate of a size-structure competitive system [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(7): 21-29.
[13] 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.
[14] XIAO Di, JIN Wen-wen. Pricing strategy for supply chain considering horizontal competition under C2B mode [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(5): 53-60.
[15] LI Guo-cheng, WANG Ji-xia. Calibrating option pricing models with cross entropy bat algorithm [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 80-89.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!