Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model
The global asymptotic behavior of a nonautonomous competitor-competitor-mutualist model is investigated, where all the coefficients are time-dependent and asymptotically approach periodic functions, respectively. Under certain conditions, it is shown that the limit periodic system of this asymptotic...
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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/10.1155/2013/812357 |
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| _version_ | 1832562928227713024 |
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| author | Shengmao Fu Fei Qu |
| author_facet | Shengmao Fu Fei Qu |
| author_sort | Shengmao Fu |
| collection | DOAJ |
| description | The global asymptotic behavior of a nonautonomous competitor-competitor-mutualist model is investigated, where all the coefficients are time-dependent and asymptotically approach periodic functions, respectively. Under certain conditions, it is shown that the limit periodic system of this asymptotically periodic model admits two positive periodic solutions (u1T,u2T,u3T), (u1T,u2T,u3T) such that uiT≤uiT (i=1,2,3), and the sector {(u1,u2,u3):uiT≤ui≤uiT, i=1,2,3} is a global attractor of the asymptotically periodic model. In particular, we derive sufficient conditions that guarantee the existence of a positive periodic solution which is globally asymptotically stable. |
| format | Article |
| id | doaj-art-165e5b9db0294e3d808ecc9d05121385 |
| 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-165e5b9db0294e3d808ecc9d051213852025-02-03T01:21:25ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/812357812357Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist ModelShengmao Fu0Fei Qu1College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaThe global asymptotic behavior of a nonautonomous competitor-competitor-mutualist model is investigated, where all the coefficients are time-dependent and asymptotically approach periodic functions, respectively. Under certain conditions, it is shown that the limit periodic system of this asymptotically periodic model admits two positive periodic solutions (u1T,u2T,u3T), (u1T,u2T,u3T) such that uiT≤uiT (i=1,2,3), and the sector {(u1,u2,u3):uiT≤ui≤uiT, i=1,2,3} is a global attractor of the asymptotically periodic model. In particular, we derive sufficient conditions that guarantee the existence of a positive periodic solution which is globally asymptotically stable.http://dx.doi.org/10.1155/2013/812357 |
| spellingShingle | Shengmao Fu Fei Qu Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model Abstract and Applied Analysis |
| title | Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model |
| title_full | Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model |
| title_fullStr | Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model |
| title_full_unstemmed | Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model |
| title_short | Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model |
| title_sort | global asymptotic behavior of a nonautonomous competitor competitor mutualist model |
| url | http://dx.doi.org/10.1155/2013/812357 |
| work_keys_str_mv | AT shengmaofu globalasymptoticbehaviorofanonautonomouscompetitorcompetitormutualistmodel AT feiqu globalasymptoticbehaviorofanonautonomouscompetitorcompetitormutualistmodel |