Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback Control
A nonautonomous discrete two-species Lotka-Volterra competition system with infinite delays and single feedback control is considered in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. Also, by construc...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/867313 |
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| _version_ | 1832548968174714880 |
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| author | Liang Zhao Xiangdong Xie Liya Yang Fengde Chen |
| author_facet | Liang Zhao Xiangdong Xie Liya Yang Fengde Chen |
| author_sort | Liang Zhao |
| collection | DOAJ |
| description | A nonautonomous discrete two-species Lotka-Volterra competition system with infinite delays and single feedback control is considered in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the global attractivity and extinction of the system are obtained. It is shown that if the the discrete Lotka-Volterra competitive system with infinite delays and without feedback control is permanent, then, by choosing some suitable feedback control variable, the permanent species will be driven to extinction. That is, the feedback control variable, which represents the biological control or some harvesting procedure, is the unstable factor of the system. Such a finding overturns the previous scholars’ recognition on feedback control variables. |
| format | Article |
| id | doaj-art-aeb4891bbabb47ee9031d12146e2de0e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-aeb4891bbabb47ee9031d12146e2de0e2025-02-03T06:12:32ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/867313867313Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback ControlLiang Zhao0Xiangdong Xie1Liya Yang2Fengde Chen3College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350116, ChinaDepartment of Mathematics, Ningde Normal University, Fujian 352100, ChinaCollege of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350116, ChinaCollege of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350116, ChinaA nonautonomous discrete two-species Lotka-Volterra competition system with infinite delays and single feedback control is considered in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the global attractivity and extinction of the system are obtained. It is shown that if the the discrete Lotka-Volterra competitive system with infinite delays and without feedback control is permanent, then, by choosing some suitable feedback control variable, the permanent species will be driven to extinction. That is, the feedback control variable, which represents the biological control or some harvesting procedure, is the unstable factor of the system. Such a finding overturns the previous scholars’ recognition on feedback control variables.http://dx.doi.org/10.1155/2014/867313 |
| spellingShingle | Liang Zhao Xiangdong Xie Liya Yang Fengde Chen Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback Control Abstract and Applied Analysis |
| title | Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback Control |
| title_full | Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback Control |
| title_fullStr | Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback Control |
| title_full_unstemmed | Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback Control |
| title_short | Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback Control |
| title_sort | dynamic behaviors of a discrete lotka volterra competition system with infinite delays and single feedback control |
| url | http://dx.doi.org/10.1155/2014/867313 |
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