Analysis of a Nonautonomous Delayed Predator-Prey System with a Stage Structure for the Predator in a Polluted Environment
A two-species nonautonomous Lotka-Volterra type model with diffusional migration among the immature predator population, constant delay among the matured predators, and toxicant effect on the immature predators in a nonprotective patch is proposed. The scale of the protective zone among the immature...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/891812 |
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| _version_ | 1832545655540678656 |
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| author | G. P. Samanta |
| author_facet | G. P. Samanta |
| author_sort | G. P. Samanta |
| collection | DOAJ |
| description | A two-species nonautonomous Lotka-Volterra type model with diffusional migration among the immature predator population, constant delay among the matured predators, and toxicant effect on the immature predators in a nonprotective patch is proposed. The scale of the protective zone among the immature predator population can be regulated through diffusive coefficients Di(t), i=1,2. It is proved that this system is uniformly persistent (permanence) under appropriate
conditions. Sufficient conditions are derived to confirm that if this system admits a
positive periodic solution, then it is globally asymptotically stable. |
| format | Article |
| id | doaj-art-8bbc717eb4e0474baa7cf48c9416f0b2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8bbc717eb4e0474baa7cf48c9416f0b22025-02-03T07:25:05ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/891812891812Analysis of a Nonautonomous Delayed Predator-Prey System with a Stage Structure for the Predator in a Polluted EnvironmentG. P. Samanta0Mathematical Institute, Slovak Academy of Sciences, Stefanikova 49, 81473 Bratislava, SlovakiaA two-species nonautonomous Lotka-Volterra type model with diffusional migration among the immature predator population, constant delay among the matured predators, and toxicant effect on the immature predators in a nonprotective patch is proposed. The scale of the protective zone among the immature predator population can be regulated through diffusive coefficients Di(t), i=1,2. It is proved that this system is uniformly persistent (permanence) under appropriate conditions. Sufficient conditions are derived to confirm that if this system admits a positive periodic solution, then it is globally asymptotically stable.http://dx.doi.org/10.1155/2010/891812 |
| spellingShingle | G. P. Samanta Analysis of a Nonautonomous Delayed Predator-Prey System with a Stage Structure for the Predator in a Polluted Environment International Journal of Mathematics and Mathematical Sciences |
| title | Analysis of a Nonautonomous Delayed Predator-Prey System with a Stage Structure for the Predator in a Polluted Environment |
| title_full | Analysis of a Nonautonomous Delayed Predator-Prey System with a Stage Structure for the Predator in a Polluted Environment |
| title_fullStr | Analysis of a Nonautonomous Delayed Predator-Prey System with a Stage Structure for the Predator in a Polluted Environment |
| title_full_unstemmed | Analysis of a Nonautonomous Delayed Predator-Prey System with a Stage Structure for the Predator in a Polluted Environment |
| title_short | Analysis of a Nonautonomous Delayed Predator-Prey System with a Stage Structure for the Predator in a Polluted Environment |
| title_sort | analysis of a nonautonomous delayed predator prey system with a stage structure for the predator in a polluted environment |
| url | http://dx.doi.org/10.1155/2010/891812 |
| work_keys_str_mv | AT gpsamanta analysisofanonautonomousdelayedpredatorpreysystemwithastagestructureforthepredatorinapollutedenvironment |