Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays
In this paper, we study the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global ex...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2018-01-01
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| Series: | Journal of Biological Dynamics |
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| Online Access: | http://dx.doi.org/10.1080/17513758.2018.1467048 |
| _version_ | 1818985733300420608 |
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| author | Kaihong Zhao |
| author_facet | Kaihong Zhao |
| author_sort | Kaihong Zhao |
| collection | DOAJ |
| description | In this paper, we study the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results. |
| first_indexed | 2024-12-20T18:39:35Z |
| format | Article |
| id | doaj.art-259916866d7d448e890b52dbcfbb4f98 |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-12-20T18:39:35Z |
| publishDate | 2018-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-259916866d7d448e890b52dbcfbb4f982022-12-21T19:29:51ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662018-01-0112143345410.1080/17513758.2018.14670481467048Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delaysKaihong Zhao0Kunming University of Science and TechnologyIn this paper, we study the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.http://dx.doi.org/10.1080/17513758.2018.1467048global exponential stabilityimpulsive gilpin–ayala competition modeldiscrete and distributed time delaysfixed point theorem on coneslyapunov functional |
| spellingShingle | Kaihong Zhao Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays Journal of Biological Dynamics global exponential stability impulsive gilpin–ayala competition model discrete and distributed time delays fixed point theorem on cones lyapunov functional |
| title | Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays |
| title_full | Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays |
| title_fullStr | Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays |
| title_full_unstemmed | Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays |
| title_short | Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays |
| title_sort | global exponential stability of positive periodic solution of the n species impulsive gilpin ayala competition model with discrete and distributed time delays |
| topic | global exponential stability impulsive gilpin–ayala competition model discrete and distributed time delays fixed point theorem on cones lyapunov functional |
| url | http://dx.doi.org/10.1080/17513758.2018.1467048 |
| work_keys_str_mv | AT kaihongzhao globalexponentialstabilityofpositiveperiodicsolutionofthenspeciesimpulsivegilpinayalacompetitionmodelwithdiscreteanddistributedtimedelays |