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Dynamical analysis of a fuzzy phytoplankton-zooplankton model with refuge, fishery protection and harvesting
Meng, Xin-You; Wu, Yu-Qian
2020-02-04
发表期刊JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
ISSN1598-5865
卷号63期号:1-2页码:361-389
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.
关键词Fuzzy parameters Phytoplankton-zooplankton model Utility function method Hopf bifurcation Pontryagin's maximum principle
DOI10.1007/s12190-020-01321-y
收录类别SCI
语种英语
资助项目National Natural Science Foundation of China[11661050,11861044]
WOS研究方向Mathematics
WOS类目Mathematics, Applied ; Mathematics
WOS记录号WOS:000511075300001
出版者SPRINGER HEIDELBERG
引用统计
被引频次:19[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符https://ir.lut.edu.cn/handle/2XXMBERH/64256
专题理学院
通讯作者Meng, Xin-You
作者单位Lanzhou Univ Technol, Sch Sci, Lanzhou 730050, Gansu, Peoples R China
第一作者单位理学院
通讯作者单位理学院
第一作者的第一单位理学院
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.
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