Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays
This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/936952 |
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| _version_ | 1832564665429786624 |
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| author | Wenzhen Gan Canrong Tian Qunying Zhang Zhigui Lin |
| author_facet | Wenzhen Gan Canrong Tian Qunying Zhang Zhigui Lin |
| author_sort | Wenzhen Gan |
| collection | DOAJ |
| description | This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show that intraspecific competition benefits the coexistence of prey and predator. Furthermore, the introduction of Michaelis-Menten type functional response positively affects the coexistence of prey and predator, and the nonlocal delay is harmless for stabilities of all nonnegative steady states of the system. Numerical simulations are carried out to illustrate the main results. |
| format | Article |
| id | doaj-art-1add3babf21d4acb909f68c1481731e9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1add3babf21d4acb909f68c1481731e92025-02-03T01:10:24ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/936952936952Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal DelaysWenzhen Gan0Canrong Tian1Qunying Zhang2Zhigui Lin3School of Mathematics and Physics, Jiangsu Teachers University of Technology, Changzhou 213001, ChinaBasic Department, Yancheng Institute of Technology, Yangcheng 224003, ChinaSchool of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaSchool of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaThis paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show that intraspecific competition benefits the coexistence of prey and predator. Furthermore, the introduction of Michaelis-Menten type functional response positively affects the coexistence of prey and predator, and the nonlocal delay is harmless for stabilities of all nonnegative steady states of the system. Numerical simulations are carried out to illustrate the main results.http://dx.doi.org/10.1155/2013/936952 |
| spellingShingle | Wenzhen Gan Canrong Tian Qunying Zhang Zhigui Lin Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays Abstract and Applied Analysis |
| title | Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays |
| title_full | Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays |
| title_fullStr | Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays |
| title_full_unstemmed | Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays |
| title_short | Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays |
| title_sort | stability in a simple food chain system with michaelis menten functional response and nonlocal delays |
| url | http://dx.doi.org/10.1155/2013/936952 |
| work_keys_str_mv | AT wenzhengan stabilityinasimplefoodchainsystemwithmichaelismentenfunctionalresponseandnonlocaldelays AT canrongtian stabilityinasimplefoodchainsystemwithmichaelismentenfunctionalresponseandnonlocaldelays AT qunyingzhang stabilityinasimplefoodchainsystemwithmichaelismentenfunctionalresponseandnonlocaldelays AT zhiguilin stabilityinasimplefoodchainsystemwithmichaelismentenfunctionalresponseandnonlocaldelays |