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Stability and Hopf bifurcation analysis of a delayed phytoplankton-zooplankton model with Allee effect and linear harvesting
Meng, Xinyou; Li, Jie
2020
Source PublicationMATHEMATICAL BIOSCIENCES AND ENGINEERING
ISSN1547-1063
Volume17Issue:3Pages:1973-2002
AbstractIn this article, a delayed phytoplankton-zooplankton system with Allee effect and linear harvesting is proposed, where phytoplankton species protects themselves from zooplankton by producing toxin and taking shelter. First, the existence and stability of the possible equilibria of system are explored. Next, the existence of Hopf bifurcation is investigated when the system has no time delay. What's more, the stability of limit cycle is demonstrated by calculating the first Lyapunov number. Then, the condition that Hopf bifurcation occurs is obtained by taking the time delay describing the maturation period of zooplankton species as a bifurcation parameter. Furthermore, based on the normal form theory and the central manifold theorem, we derive the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. In addition, by regarding the harvesting effort as control variable and employing the Pontryagin's Maximum Principle, the optimal harvesting strategy of the system is obtained. Finally, in order to verify the validity of the theoretical results, some numerical simulations are carried out.
Keywordphytoplankton-zooplankton model Allee effect time delay Hopf bifurcation
DOI10.3934/mbe.2020105
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[11661050][11861044]
WOS Research AreaMathematical & Computational Biology
WOS SubjectMathematical & Computational Biology
WOS IDWOS:000519873900005
PublisherAMER INST MATHEMATICAL SCIENCES-AIMS
Citation statistics
Cited Times:11[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.lut.edu.cn/handle/2XXMBERH/64201
Collection理学院
Corresponding AuthorMeng, Xinyou
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, Xinyou,Li, Jie. Stability and Hopf bifurcation analysis of a delayed phytoplankton-zooplankton model with Allee effect and linear harvesting[J]. MATHEMATICAL BIOSCIENCES AND ENGINEERING,2020,17(3):1973-2002.
APA Meng, Xinyou,&Li, Jie.(2020).Stability and Hopf bifurcation analysis of a delayed phytoplankton-zooplankton model with Allee effect and linear harvesting.MATHEMATICAL BIOSCIENCES AND ENGINEERING,17(3),1973-2002.
MLA Meng, Xinyou,et al."Stability and Hopf bifurcation analysis of a delayed phytoplankton-zooplankton model with Allee effect and linear harvesting".MATHEMATICAL BIOSCIENCES AND ENGINEERING 17.3(2020):1973-2002.
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