Dynamic Behaviors of a General Discrete Nonautonomous System of Plankton Allelopathy with Delays
We study the dynamic behaviors of a general discrete nonautonomous system of plankton allelopathy with delays. We first show that under some suitable assumption, the system is permanent. Next, by constructing a suitable Lyapunov functional, we obtain a set of sufficient conditions which guarantee th...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/310425 |
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| _version_ | 1832549035039260672 |
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| author | Yaoping Chen Fengde Chen Zhong Li |
| author_facet | Yaoping Chen Fengde Chen Zhong Li |
| author_sort | Yaoping Chen |
| collection | DOAJ |
| description | We study the dynamic behaviors of a general discrete nonautonomous system of plankton allelopathy with delays. We first show that under some suitable assumption, the system is permanent. Next, by constructing a suitable Lyapunov functional, we obtain a set of sufficient conditions which guarantee the global attractivity of the two species. After that, by constructing an extinction-type Lyapunov functional, we show that under some suitable assumptions, one species will be driven to extinction. Finally, two examples together with their numerical simulations show the feasibility of the main results. |
| format | Article |
| id | doaj-art-6cce275227f44ac1bf837526fc0d35ec |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-6cce275227f44ac1bf837526fc0d35ec2025-02-03T06:12:22ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/310425310425Dynamic Behaviors of a General Discrete Nonautonomous System of Plankton Allelopathy with DelaysYaoping Chen0Fengde Chen1Zhong Li2College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, ChinaCollege of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, ChinaCollege of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, ChinaWe study the dynamic behaviors of a general discrete nonautonomous system of plankton allelopathy with delays. We first show that under some suitable assumption, the system is permanent. Next, by constructing a suitable Lyapunov functional, we obtain a set of sufficient conditions which guarantee the global attractivity of the two species. After that, by constructing an extinction-type Lyapunov functional, we show that under some suitable assumptions, one species will be driven to extinction. Finally, two examples together with their numerical simulations show the feasibility of the main results.http://dx.doi.org/10.1155/2008/310425 |
| spellingShingle | Yaoping Chen Fengde Chen Zhong Li Dynamic Behaviors of a General Discrete Nonautonomous System of Plankton Allelopathy with Delays Discrete Dynamics in Nature and Society |
| title | Dynamic Behaviors of a General Discrete Nonautonomous System of Plankton Allelopathy with Delays |
| title_full | Dynamic Behaviors of a General Discrete Nonautonomous System of Plankton Allelopathy with Delays |
| title_fullStr | Dynamic Behaviors of a General Discrete Nonautonomous System of Plankton Allelopathy with Delays |
| title_full_unstemmed | Dynamic Behaviors of a General Discrete Nonautonomous System of Plankton Allelopathy with Delays |
| title_short | Dynamic Behaviors of a General Discrete Nonautonomous System of Plankton Allelopathy with Delays |
| title_sort | dynamic behaviors of a general discrete nonautonomous system of plankton allelopathy with delays |
| url | http://dx.doi.org/10.1155/2008/310425 |
| work_keys_str_mv | AT yaopingchen dynamicbehaviorsofageneraldiscretenonautonomoussystemofplanktonallelopathywithdelays AT fengdechen dynamicbehaviorsofageneraldiscretenonautonomoussystemofplanktonallelopathywithdelays AT zhongli dynamicbehaviorsofageneraldiscretenonautonomoussystemofplanktonallelopathywithdelays |