Bifurcation analysis and optimal control of a delayed single-species fishery economic model
In this paper, a single-species fishery economic model with two time delays is investigated. The system is shown to be locally stable around the interior equilibrium when the parameters are in a specific range, and the Hopf bifurcation is shown occur as the time delays cross the critical values. The...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-06-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2022378?viewType=HTML |
| _version_ | 1811332156233875456 |
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| author | Xin Gao Yue Zhang |
| author_facet | Xin Gao Yue Zhang |
| author_sort | Xin Gao |
| collection | DOAJ |
| description | In this paper, a single-species fishery economic model with two time delays is investigated. The system is shown to be locally stable around the interior equilibrium when the parameters are in a specific range, and the Hopf bifurcation is shown occur as the time delays cross the critical values. Then the direction of Hopf bifurcation and the stability of bifurcated periodic solutions are discussed. In addition, the optimal cost strategy is obtained to maximize the net profit and minimize the waste by hoarding for speculation. We also design controls to minimize the waste by hoarding for the speculation of the system with time delays. The existence of the optimal controls and derivation from the optimality conditions are discussed. The validity of the theoretical results are shown via numerical simulation. |
| first_indexed | 2024-04-13T16:32:28Z |
| format | Article |
| id | doaj.art-76f473d74ea74740879d0d9cd43e6bd3 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-13T16:32:28Z |
| publishDate | 2022-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-76f473d74ea74740879d0d9cd43e6bd32022-12-22T02:39:32ZengAIMS PressMathematical Biosciences and Engineering1551-00182022-06-011988081810610.3934/mbe.2022378Bifurcation analysis and optimal control of a delayed single-species fishery economic modelXin Gao 0Yue Zhang1College of Sciences, Northeastern University, Shenyang 110004, ChinaCollege of Sciences, Northeastern University, Shenyang 110004, ChinaIn this paper, a single-species fishery economic model with two time delays is investigated. The system is shown to be locally stable around the interior equilibrium when the parameters are in a specific range, and the Hopf bifurcation is shown occur as the time delays cross the critical values. Then the direction of Hopf bifurcation and the stability of bifurcated periodic solutions are discussed. In addition, the optimal cost strategy is obtained to maximize the net profit and minimize the waste by hoarding for speculation. We also design controls to minimize the waste by hoarding for the speculation of the system with time delays. The existence of the optimal controls and derivation from the optimality conditions are discussed. The validity of the theoretical results are shown via numerical simulation.https://www.aimspress.com/article/doi/10.3934/mbe.2022378?viewType=HTMLfishery economic modeltime delayshopf bifurcationoptimal control |
| spellingShingle | Xin Gao Yue Zhang Bifurcation analysis and optimal control of a delayed single-species fishery economic model Mathematical Biosciences and Engineering fishery economic model time delays hopf bifurcation optimal control |
| title | Bifurcation analysis and optimal control of a delayed single-species fishery economic model |
| title_full | Bifurcation analysis and optimal control of a delayed single-species fishery economic model |
| title_fullStr | Bifurcation analysis and optimal control of a delayed single-species fishery economic model |
| title_full_unstemmed | Bifurcation analysis and optimal control of a delayed single-species fishery economic model |
| title_short | Bifurcation analysis and optimal control of a delayed single-species fishery economic model |
| title_sort | bifurcation analysis and optimal control of a delayed single species fishery economic model |
| topic | fishery economic model time delays hopf bifurcation optimal control |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2022378?viewType=HTML |
| work_keys_str_mv | AT xingao bifurcationanalysisandoptimalcontrolofadelayedsinglespeciesfisheryeconomicmodel AT yuezhang bifurcationanalysisandoptimalcontrolofadelayedsinglespeciesfisheryeconomicmodel |