Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls
A discrete allelopathic phytoplankton model with infinite delays and feedback controls is studied in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantees the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapuno...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/7023075 |
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| _version_ | 1850156877918240768 |
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| author | Liang Zhao Bin Qin Fengde Chen |
| author_facet | Liang Zhao Bin Qin Fengde Chen |
| author_sort | Liang Zhao |
| collection | DOAJ |
| description | A discrete allelopathic phytoplankton model with infinite delays and feedback controls is studied in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantees the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the extinction of the system are obtained. Our results extend and supplement some known results and show that the feedback controls and toxic substances play a crucial role on the permanence and extinction of the system. |
| format | Article |
| id | doaj-art-329d76cd4f1240f4ab45c5ff129c6828 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-329d76cd4f1240f4ab45c5ff129c68282025-08-20T02:24:22ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/70230757023075Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback ControlsLiang Zhao0Bin Qin1Fengde Chen2School of Mathematics and Informatics, Fujian Normal University, Fuzhou, Fujian 350117, ChinaCollege of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, ChinaCollege of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350116, ChinaA discrete allelopathic phytoplankton model with infinite delays and feedback controls is studied in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantees the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the extinction of the system are obtained. Our results extend and supplement some known results and show that the feedback controls and toxic substances play a crucial role on the permanence and extinction of the system.http://dx.doi.org/10.1155/2020/7023075 |
| spellingShingle | Liang Zhao Bin Qin Fengde Chen Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls Discrete Dynamics in Nature and Society |
| title | Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls |
| title_full | Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls |
| title_fullStr | Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls |
| title_full_unstemmed | Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls |
| title_short | Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls |
| title_sort | dynamics of a discrete allelopathic phytoplankton model with infinite delays and feedback controls |
| url | http://dx.doi.org/10.1155/2020/7023075 |
| work_keys_str_mv | AT liangzhao dynamicsofadiscreteallelopathicphytoplanktonmodelwithinfinitedelaysandfeedbackcontrols AT binqin dynamicsofadiscreteallelopathicphytoplanktonmodelwithinfinitedelaysandfeedbackcontrols AT fengdechen dynamicsofadiscreteallelopathicphytoplanktonmodelwithinfinitedelaysandfeedbackcontrols |