The Bifurcation and Control of a Single-Species Fish Population Logistic Model with the Invasion of Alien Species
The objective of this paper is to study systematically the bifurcation and control of a single-species fish population logistic model with the invasion of alien species based on the theory of singular system and bifurcation. It regards Spartina anglica as an invasive species, which invades the fishe...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/548384 |
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| _version_ | 1832559979784044544 |
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| author | Yi Zhang Qiaoling Zhang Jinghao Li Qingling Zhang |
| author_facet | Yi Zhang Qiaoling Zhang Jinghao Li Qingling Zhang |
| author_sort | Yi Zhang |
| collection | DOAJ |
| description | The objective of this paper is to study systematically the bifurcation and control of a single-species fish population logistic model with the invasion of alien species based on the theory of singular system and bifurcation. It regards Spartina anglica as an invasive species, which invades the fisheries and aquaculture. Firstly, the stabilities of equilibria in this model are discussed. Moreover, the sufficient conditions for existence of the trans-critical bifurcation and the singularity induced bifurcation are obtained. Secondly, the state feedback controller is designed to eliminate the unexpected singularity induced bifurcation by combining harvested effort with the purification capacity. It obviously inhibits the switch of population and makes the system stable. Finally, the numerical simulation is proposed to show the practical significance of the bifurcation and control from the biological point of view. |
| format | Article |
| id | doaj-art-797088293b214617a3d2af676678a165 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-797088293b214617a3d2af676678a1652025-02-03T01:28:40ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/548384548384The Bifurcation and Control of a Single-Species Fish Population Logistic Model with the Invasion of Alien SpeciesYi Zhang0Qiaoling Zhang1Jinghao Li2Qingling Zhang3School of Science, Shenyang University of Technology, Shenyang 110870, ChinaSchool of Science, Shenyang University of Technology, Shenyang 110870, ChinaInstitute of Systems Science, Northeastern University, Shenyang 110819, ChinaInstitute of Systems Science, Northeastern University, Shenyang 110819, ChinaThe objective of this paper is to study systematically the bifurcation and control of a single-species fish population logistic model with the invasion of alien species based on the theory of singular system and bifurcation. It regards Spartina anglica as an invasive species, which invades the fisheries and aquaculture. Firstly, the stabilities of equilibria in this model are discussed. Moreover, the sufficient conditions for existence of the trans-critical bifurcation and the singularity induced bifurcation are obtained. Secondly, the state feedback controller is designed to eliminate the unexpected singularity induced bifurcation by combining harvested effort with the purification capacity. It obviously inhibits the switch of population and makes the system stable. Finally, the numerical simulation is proposed to show the practical significance of the bifurcation and control from the biological point of view.http://dx.doi.org/10.1155/2014/548384 |
| spellingShingle | Yi Zhang Qiaoling Zhang Jinghao Li Qingling Zhang The Bifurcation and Control of a Single-Species Fish Population Logistic Model with the Invasion of Alien Species Discrete Dynamics in Nature and Society |
| title | The Bifurcation and Control of a Single-Species Fish Population Logistic Model with the Invasion of Alien Species |
| title_full | The Bifurcation and Control of a Single-Species Fish Population Logistic Model with the Invasion of Alien Species |
| title_fullStr | The Bifurcation and Control of a Single-Species Fish Population Logistic Model with the Invasion of Alien Species |
| title_full_unstemmed | The Bifurcation and Control of a Single-Species Fish Population Logistic Model with the Invasion of Alien Species |
| title_short | The Bifurcation and Control of a Single-Species Fish Population Logistic Model with the Invasion of Alien Species |
| title_sort | bifurcation and control of a single species fish population logistic model with the invasion of alien species |
| url | http://dx.doi.org/10.1155/2014/548384 |
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