Global Stability for a Semidiscrete Logistic System with Feedback Control
In this paper, a semidiscrete logistic model with the Dirichlet boundary conditions and feedback controls is proposed. By means of the sub- and supper-solution method and eigenvalue theory, the unique positive equilibrium is proved. By constructing a suitable Lyapunov function, the global asymptomat...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/3189515 |
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| _version_ | 1832566100324253696 |
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| author | Li Xu Shanshan Lou Ruiwen Han |
| author_facet | Li Xu Shanshan Lou Ruiwen Han |
| author_sort | Li Xu |
| collection | DOAJ |
| description | In this paper, a semidiscrete logistic model with the Dirichlet boundary conditions and feedback controls is proposed. By means of the sub- and supper-solution method and eigenvalue theory, the unique positive equilibrium is proved. By constructing a suitable Lyapunov function, 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-df146cc9051c441eb1d241b3fcccf34c |
| institution | Kabale University |
| 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-df146cc9051c441eb1d241b3fcccf34c2025-02-03T01:05:06ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/31895153189515Global Stability for a Semidiscrete Logistic System with Feedback ControlLi Xu0Shanshan Lou1Ruiwen Han2School of Mathematics, Tianjin University, Tianjin 300072, ChinaSchool of Science, Tianjin University of Commerce, Tianjin 300134, ChinaSchool of Science, Tianjin University of Commerce, Tianjin 300134, ChinaIn this paper, a semidiscrete logistic model with the Dirichlet boundary conditions and feedback controls is proposed. By means of the sub- and supper-solution method and eigenvalue theory, the unique positive equilibrium is proved. By constructing a suitable Lyapunov function, 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/10.1155/2020/3189515 |
| spellingShingle | Li Xu Shanshan Lou Ruiwen Han Global Stability for a Semidiscrete Logistic System with Feedback Control Discrete Dynamics in Nature and Society |
| title | Global Stability for a Semidiscrete Logistic System with Feedback Control |
| title_full | Global Stability for a Semidiscrete Logistic System with Feedback Control |
| title_fullStr | Global Stability for a Semidiscrete Logistic System with Feedback Control |
| title_full_unstemmed | Global Stability for a Semidiscrete Logistic System with Feedback Control |
| title_short | Global Stability for a Semidiscrete Logistic System with Feedback Control |
| title_sort | global stability for a semidiscrete logistic system with feedback control |
| url | http://dx.doi.org/10.1155/2020/3189515 |
| work_keys_str_mv | AT lixu globalstabilityforasemidiscretelogisticsystemwithfeedbackcontrol AT shanshanlou globalstabilityforasemidiscretelogisticsystemwithfeedbackcontrol AT ruiwenhan globalstabilityforasemidiscretelogisticsystemwithfeedbackcontrol |