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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
Source PublicationJOURNAL OF APPLIED MATHEMATICS AND COMPUTING
ISSN1598-5865
AbstractIn 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.
KeywordFuzzy parameters Phytoplankton-zooplankton model Utility function method Hopf bifurcation Pontryagin's maximum principle
DOI10.1007/s12190-020-01321-y
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[11661050,11861044]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000511075300001
PublisherSPRINGER HEIDELBERG
Document Type期刊论文
Identifierhttp://ir.lut.edu.cn/handle/2XXMBERH/64256
Collection理学院
Corresponding AuthorMeng, Xin-You
AffiliationLanzhou Univ Technol, Sch Sci, Lanzhou 730050, Gansu, Peoples R China
First Author AffilicationColl Sci
Corresponding Author AffilicationColl Sci
First Signature AffilicationColl Sci
Recommended Citation
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.
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.
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 (2020).
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