Evolution of Lotka-Volterra predator-prey systems under telegraph noise
In this paper we study a Lotka-Volterra predator-prey system with prey logisticgrowth under the telegraph noise. The telegraph noise switches at random two prey-predator models. The aim of this work is to determinethe subset of omega-limit set of the system and show out the existence of a stationar...
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| Language: | English |
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AIMS Press
2009-08-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.683 |
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| author | P. Auger N. H. Du N. T. Hieu |
| author_facet | P. Auger N. H. Du N. T. Hieu |
| author_sort | P. Auger |
| collection | DOAJ |
| description | In this paper we study a Lotka-Volterra predator-prey system with prey logisticgrowth under the telegraph noise. The telegraph noise switches at random two prey-predator models. The aim of this work is to determinethe subset of omega-limit set of the system and show out the existence of a stationarydistribution. We also focus on persistence of the predator and thus we look forconditions that allow persistence of the predator and prey community. We showthat the asymptotic behaviour highly depends on the value of some constant$\lambda$ which is useful to make suitable predictions aboutthe persistence of the system. |
| format | Article |
| id | doaj-art-84eafd19f9c148f79a8fb1e0df0c2613 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-84eafd19f9c148f79a8fb1e0df0c26132025-01-24T02:00:01ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-08-016468370010.3934/mbe.2009.6.683Evolution of Lotka-Volterra predator-prey systems under telegraph noiseP. Auger0N. H. Du1N. T. Hieu2IRD, UMI 209, UMMISCO, IRD France Nord, F-93143, BondyIRD, UMI 209, UMMISCO, IRD France Nord, F-93143, BondyIRD, UMI 209, UMMISCO, IRD France Nord, F-93143, BondyIn this paper we study a Lotka-Volterra predator-prey system with prey logisticgrowth under the telegraph noise. The telegraph noise switches at random two prey-predator models. The aim of this work is to determinethe subset of omega-limit set of the system and show out the existence of a stationarydistribution. We also focus on persistence of the predator and thus we look forconditions that allow persistence of the predator and prey community. We showthat the asymptotic behaviour highly depends on the value of some constant$\lambda$ which is useful to make suitable predictions aboutthe persistence of the system.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.683carrying capacitytelegraph noisestationary distribution.lotka-volterra predator-prey systems |
| spellingShingle | P. Auger N. H. Du N. T. Hieu Evolution of Lotka-Volterra predator-prey systems under telegraph noise Mathematical Biosciences and Engineering carrying capacity telegraph noise stationary distribution. lotka-volterra predator-prey systems |
| title | Evolution of Lotka-Volterra predator-prey systems under telegraph noise |
| title_full | Evolution of Lotka-Volterra predator-prey systems under telegraph noise |
| title_fullStr | Evolution of Lotka-Volterra predator-prey systems under telegraph noise |
| title_full_unstemmed | Evolution of Lotka-Volterra predator-prey systems under telegraph noise |
| title_short | Evolution of Lotka-Volterra predator-prey systems under telegraph noise |
| title_sort | evolution of lotka volterra predator prey systems under telegraph noise |
| topic | carrying capacity telegraph noise stationary distribution. lotka-volterra predator-prey systems |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.683 |
| work_keys_str_mv | AT pauger evolutionoflotkavolterrapredatorpreysystemsundertelegraphnoise AT nhdu evolutionoflotkavolterrapredatorpreysystemsundertelegraphnoise AT nthieu evolutionoflotkavolterrapredatorpreysystemsundertelegraphnoise |