Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System
A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/381750 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832566540805865472 |
|---|---|
| author | Wenjie Qin Zhijun Liu |
| author_facet | Wenjie Qin Zhijun Liu |
| author_sort | Wenjie Qin |
| collection | DOAJ |
| description | A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of
coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results. |
| format | Article |
| id | doaj-art-5fbed1ff31934ca0856cfb9669861dcf |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-5fbed1ff31934ca0856cfb9669861dcf2025-02-03T01:03:50ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/381750381750Permanence and Positive Periodic Solutions of a Discrete Delay Competitive SystemWenjie Qin0Zhijun Liu1Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, ChinaDepartment of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, ChinaA discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.http://dx.doi.org/10.1155/2010/381750 |
| spellingShingle | Wenjie Qin Zhijun Liu Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System Discrete Dynamics in Nature and Society |
| title | Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System |
| title_full | Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System |
| title_fullStr | Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System |
| title_full_unstemmed | Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System |
| title_short | Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System |
| title_sort | permanence and positive periodic solutions of a discrete delay competitive system |
| url | http://dx.doi.org/10.1155/2010/381750 |
| work_keys_str_mv | AT wenjieqin permanenceandpositiveperiodicsolutionsofadiscretedelaycompetitivesystem AT zhijunliu permanenceandpositiveperiodicsolutionsofadiscretedelaycompetitivesystem |