Stability and Hopf bifurcation analysis of a delayed phytoplankton-zooplankton model with Allee effect and linear harvesting | |
Meng, Xinyou; Li, Jie | |
2020 | |
发表期刊 | MATHEMATICAL BIOSCIENCES AND ENGINEERING |
ISSN | 1547-1063 |
卷号 | 17期号:3页码:1973-2002 |
摘要 | In 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. |
关键词 | phytoplankton-zooplankton model Allee effect time delay Hopf bifurcation |
DOI | 10.3934/mbe.2020105 |
收录类别 | SCI ; SCIE ; EI |
语种 | 英语 |
资助项目 | National Natural Science Foundation of China[11661050][11861044] |
WOS研究方向 | Mathematical & Computational Biology |
WOS类目 | Mathematical & Computational Biology |
WOS记录号 | WOS:000519873900005 |
出版者 | AMER INST MATHEMATICAL SCIENCES-AIMS |
EI入藏号 | 20201608418437 |
EI主题词 | Hopf bifurcation |
EI分类号 | 471 Marine Science and Oceanography - 713 Electronic Circuits - 821.3 Agricultural Methods - 921 Mathematics - 931 Classical Physics ; Quantum Theory ; Relativity |
来源库 | WOS |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | https://ir.lut.edu.cn/handle/2XXMBERH/64201 |
专题 | 理学院 |
通讯作者 | Meng, Xinyou |
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, 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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