Stability and traveling fronts for a food chain reaction-diffusion systems with nonlocal delays
Abstract This paper is purported to investigate a food chain reaction-diffusion predator-prey system with nonlocal delays in a bounded domain with no flux boundary condition. We investigate the global stability and find the sufficient conditions of global stability of the unique positive equilibrium...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-12-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1264-0 |
| _version_ | 1818955140092133376 |
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| author | Chenglin Li Guangchun Huang |
| author_facet | Chenglin Li Guangchun Huang |
| author_sort | Chenglin Li |
| collection | DOAJ |
| description | Abstract This paper is purported to investigate a food chain reaction-diffusion predator-prey system with nonlocal delays in a bounded domain with no flux boundary condition. We investigate the global stability and find the sufficient conditions of global stability of the unique positive equilibrium for this system. The derived results show that delays often restrain stability. Using the method of linearizing this system, we see that the zero equilibrium is unstable. Moreover, by constructing upper-lower solutions, we find that there exist traveling wavefronts which connect the zero equilibrium and positive equilibrium when the wave speed is large enough and the prey intrinsic growth rate and the death rate of the predator are relatively big. |
| first_indexed | 2024-12-20T10:33:19Z |
| format | Article |
| id | doaj.art-cad5882049934945a20e1125a6573e3b |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-20T10:33:19Z |
| publishDate | 2016-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-cad5882049934945a20e1125a6573e3b2022-12-21T19:43:41ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-12-012016111510.1186/s13660-016-1264-0Stability and traveling fronts for a food chain reaction-diffusion systems with nonlocal delaysChenglin Li0Guangchun Huang1College of Mathematics, Honghe UniversityCollege of Science, Honghe UniversityAbstract This paper is purported to investigate a food chain reaction-diffusion predator-prey system with nonlocal delays in a bounded domain with no flux boundary condition. We investigate the global stability and find the sufficient conditions of global stability of the unique positive equilibrium for this system. The derived results show that delays often restrain stability. Using the method of linearizing this system, we see that the zero equilibrium is unstable. Moreover, by constructing upper-lower solutions, we find that there exist traveling wavefronts which connect the zero equilibrium and positive equilibrium when the wave speed is large enough and the prey intrinsic growth rate and the death rate of the predator are relatively big.http://link.springer.com/article/10.1186/s13660-016-1264-0stabilitynonlocal delaytraveling waves |
| spellingShingle | Chenglin Li Guangchun Huang Stability and traveling fronts for a food chain reaction-diffusion systems with nonlocal delays Journal of Inequalities and Applications stability nonlocal delay traveling waves |
| title | Stability and traveling fronts for a food chain reaction-diffusion systems with nonlocal delays |
| title_full | Stability and traveling fronts for a food chain reaction-diffusion systems with nonlocal delays |
| title_fullStr | Stability and traveling fronts for a food chain reaction-diffusion systems with nonlocal delays |
| title_full_unstemmed | Stability and traveling fronts for a food chain reaction-diffusion systems with nonlocal delays |
| title_short | Stability and traveling fronts for a food chain reaction-diffusion systems with nonlocal delays |
| title_sort | stability and traveling fronts for a food chain reaction diffusion systems with nonlocal delays |
| topic | stability nonlocal delay traveling waves |
| url | http://link.springer.com/article/10.1186/s13660-016-1264-0 |
| work_keys_str_mv | AT chenglinli stabilityandtravelingfrontsforafoodchainreactiondiffusionsystemswithnonlocaldelays AT guangchunhuang stabilityandtravelingfrontsforafoodchainreactiondiffusionsystemswithnonlocaldelays |