Global Stability for a Discrete Space-Time Lotka–Volterra System with Feedback Control
In this paper, a discrete space-time Lotka–Volterra model with the periodic boundary conditions and feedback control is proposed. By means of a discrete version of comparison theorem, the boundedness of the nonnegative solution of the system is proved. By the combination of the Volterra-type and qua...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/2960503 |
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| _version_ | 1832566636757909504 |
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| author | Li Xu Ruiwen Han |
| author_facet | Li Xu Ruiwen Han |
| author_sort | Li Xu |
| collection | DOAJ |
| description | In this paper, a discrete space-time Lotka–Volterra model with the periodic boundary conditions and feedback control is proposed. By means of a discrete version of comparison theorem, the boundedness of the nonnegative solution of the system is proved. By the combination of the Volterra-type and quadratic Lyapunov functions, the global asymptomatic stability of the unique positive equilibrium is investigated. Finally, numerical simulations are presented to verify the effectiveness of the main results. |
| format | Article |
| id | doaj-art-bf698a1153f048709f2ed69c7c75057b |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-bf698a1153f048709f2ed69c7c75057b2025-02-03T01:03:40ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/29605032960503Global Stability for a Discrete Space-Time Lotka–Volterra System with Feedback ControlLi Xu0Ruiwen Han1School of Science, Tianjin University of Commerce, Tianjin 300134, ChinaSchool of Science, Tianjin University of Commerce, Tianjin 300134, ChinaIn this paper, a discrete space-time Lotka–Volterra model with the periodic boundary conditions and feedback control is proposed. By means of a discrete version of comparison theorem, the boundedness of the nonnegative solution of the system is proved. By the combination of the Volterra-type and quadratic Lyapunov functions, the global asymptomatic stability of the unique positive equilibrium is investigated. Finally, numerical simulations are presented to verify the effectiveness of the main results.http://dx.doi.org/10.1155/2020/2960503 |
| spellingShingle | Li Xu Ruiwen Han Global Stability for a Discrete Space-Time Lotka–Volterra System with Feedback Control Complexity |
| title | Global Stability for a Discrete Space-Time Lotka–Volterra System with Feedback Control |
| title_full | Global Stability for a Discrete Space-Time Lotka–Volterra System with Feedback Control |
| title_fullStr | Global Stability for a Discrete Space-Time Lotka–Volterra System with Feedback Control |
| title_full_unstemmed | Global Stability for a Discrete Space-Time Lotka–Volterra System with Feedback Control |
| title_short | Global Stability for a Discrete Space-Time Lotka–Volterra System with Feedback Control |
| title_sort | global stability for a discrete space time lotka volterra system with feedback control |
| url | http://dx.doi.org/10.1155/2020/2960503 |
| work_keys_str_mv | AT lixu globalstabilityforadiscretespacetimelotkavolterrasystemwithfeedbackcontrol AT ruiwenhan globalstabilityforadiscretespacetimelotkavolterrasystemwithfeedbackcontrol |