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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Main Authors: Liang Zhao, Bin Qin, Fengde Chen
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2020/7023075
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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.
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institution OA Journals
issn 1026-0226
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publishDate 2020-01-01
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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
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AT binqin dynamicsofadiscreteallelopathicphytoplanktonmodelwithinfinitedelaysandfeedbackcontrols
AT fengdechen dynamicsofadiscreteallelopathicphytoplanktonmodelwithinfinitedelaysandfeedbackcontrols