Permanence and Stability of an Age-Structured Prey-Predator System with Delays
An age-structured prey-predator model with delays is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, permanence, and stability are analyzed. By using the persistence theory for infinite-dimensional systems, the sufficient conditions for th...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2007/54861 |
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| _version_ | 1832545451430117376 |
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| author | Liming Cai Xuezhi Li Xinyu Song Jingyuan Yu |
| author_facet | Liming Cai Xuezhi Li Xinyu Song Jingyuan Yu |
| author_sort | Liming Cai |
| collection | DOAJ |
| description | An age-structured prey-predator model with delays is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, permanence, and stability are analyzed. By using the persistence theory for infinite-dimensional systems, the sufficient conditions for the permanence of the system are obtained. By constructing suitable Lyapunov functions and using an iterative technique, sufficient conditions are also obtained for the global asymptotic stability of the positive equilibrium of the model. |
| format | Article |
| id | doaj-art-8ac11cbf17034bf4b522a8b194ce9ea1 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8ac11cbf17034bf4b522a8b194ce9ea12025-02-03T07:25:45ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2007-01-01200710.1155/2007/5486154861Permanence and Stability of an Age-Structured Prey-Predator System with DelaysLiming Cai0Xuezhi Li1Xinyu Song2Jingyuan Yu3College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000, ChinaCollege of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000, ChinaCollege of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000, ChinaBeijing Institutes of Information and Control, Beijing 100037, ChinaAn age-structured prey-predator model with delays is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, permanence, and stability are analyzed. By using the persistence theory for infinite-dimensional systems, the sufficient conditions for the permanence of the system are obtained. By constructing suitable Lyapunov functions and using an iterative technique, sufficient conditions are also obtained for the global asymptotic stability of the positive equilibrium of the model.http://dx.doi.org/10.1155/2007/54861 |
| spellingShingle | Liming Cai Xuezhi Li Xinyu Song Jingyuan Yu Permanence and Stability of an Age-Structured Prey-Predator System with Delays Discrete Dynamics in Nature and Society |
| title | Permanence and Stability of an Age-Structured Prey-Predator System with Delays |
| title_full | Permanence and Stability of an Age-Structured Prey-Predator System with Delays |
| title_fullStr | Permanence and Stability of an Age-Structured Prey-Predator System with Delays |
| title_full_unstemmed | Permanence and Stability of an Age-Structured Prey-Predator System with Delays |
| title_short | Permanence and Stability of an Age-Structured Prey-Predator System with Delays |
| title_sort | permanence and stability of an age structured prey predator system with delays |
| url | http://dx.doi.org/10.1155/2007/54861 |
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