Dynamical analysis of a fuzzy phytoplankton–zooplankton model with refuge, fishery protection and harvesting

doi:10.1007/s12190-020-01321-y

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	Dynamical analysis of a fuzzy phytoplankton–zooplankton model with refuge, fishery protection and harvesting
	Meng, Xin-You; Wu, Yu-Qian
刊名	Journal of Applied Mathematics and Computing
	2020-06-01
卷号	63 期号:1-2 页码:361-389
关键词	Differential equations Fisheries Fuzzy sets Harvesting Linear control systems Nonlinear feedback Phytoplankton Plankton Profitability Bifurcation parameter Biological parameter Bionomic equilibrium Differential algebraic models Differential systems Nonlinear feedback controllers Optimal harvesting policy Triangular fuzzy numbers
ISSN号	15985865
DOI	10.1007/s12190-020-01321-y
英文摘要	In this paper, a singular phytoplankton–zooplankton model with fuzzy parameters, refuge, fishery protection and harvesting is studied by regarding the imprecise biological parameters as one form of triangular fuzzy number. By using the utility function method, the transformed differential equation is reduced to a differential equation. In absence of economic profit, the existence of positive equilibria, local stability and global stability for the interior equilibrium of the present differential system are discussed, the conditions of Hopf bifurcation occurring at the positive equilibrium are given, and the corresponding nonlinear feedback controller is designed to eliminate Hopf bifurcation. In presence of economic profit, the corresponding differential algebraic model is proposed and some conditions of the existence of the interior equilibrium are derived. By regarding economic profit as bifurcation parameter, singular induced bifurcation occurring is investigated, and a linear controller is designed to remove such bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal harvesting policy to maximize the benefit as well as conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical results after each part. Results show that imprecise parameters not only affect the interior equilibrium and the bionomic equilibrium of system, but also affect the critical value of bifurcation and branch range. © 2020, Korean Society for Informatics and Computational Applied Mathematics.
WOS研究方向	Mathematics
语种	英语
出版者	Springer Science and Business Media Deutschland GmbH
WOS记录号	WOS:000511075300001
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/115027]
专题	理学院
作者单位	School of Science, Lanzhou University of Technology, Lanzhou; Gansu; 730050, China
推荐引用方式 GB/T 7714	Meng, Xin-You,Wu, Yu-Qian. Dynamical analysis of a fuzzy phytoplankton–zooplankton model with refuge, fishery protection and harvesting[J]. Journal of Applied Mathematics and Computing,2020,63(1-2):361-389.
APA	Meng, Xin-You,&Wu, Yu-Qian.(2020).Dynamical analysis of a fuzzy phytoplankton–zooplankton model with refuge, fishery protection and harvesting.Journal of Applied Mathematics and Computing,63(1-2),361-389.
MLA	Meng, Xin-You,et al."Dynamical analysis of a fuzzy phytoplankton–zooplankton model with refuge, fishery protection and harvesting".Journal of Applied Mathematics and Computing 63.1-2(2020):361-389.