Competition and Dispersal Delays in Patchy Environments
Dispersal delays are introduced into a competition model for two species that disperse among $n$ identical patches. The model is formulated as a system of integro-differential equations with an arbitrary distribution of dispersal times between patches. By identifying steady states and analyzing lo...
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AIMS Press
2006-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.283 |
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| author | Nancy Azer P. van den Driessche |
| author_facet | Nancy Azer P. van den Driessche |
| author_sort | Nancy Azer |
| collection | DOAJ |
| description | Dispersal delays are introduced into a competition model for two species that disperse among $n$ identical patches. The model is formulated as a system of integro-differential equations with an arbitrary distribution of dispersal times between patches. By identifying steady states and analyzing local stability, conditions for competitive exclusion, coexistence or extinction are determined in terms of the system parameters. These are confirmed by numerical simulations with a delta function distribution, showing that all solutions approach a steady state and that high dispersal is generally a disadvantage to a species. However, if the two species have identical local dynamics, then small dispersal rates (with certain parameter restrictions) can be an advantage to the dispersing species. If the number of species is increased to three, then oscillatory coexistence with dispersal delay is possible. |
| format | Article |
| id | doaj-art-64d4797c1ef24a8198c6467f331d01b5 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-64d4797c1ef24a8198c6467f331d01b52025-01-24T01:51:19ZengAIMS PressMathematical Biosciences and Engineering1551-00182006-01-013228329610.3934/mbe.2006.3.283Competition and Dispersal Delays in Patchy EnvironmentsNancy Azer0P. van den Driessche1Department of Mathematics and Statistics, University of Victoria, PO BOX 3045 STN CSC, Victoria, B.C. V8W 3P4Department of Mathematics and Statistics, University of Victoria, PO BOX 3045 STN CSC, Victoria, B.C. V8W 3P4Dispersal delays are introduced into a competition model for two species that disperse among $n$ identical patches. The model is formulated as a system of integro-differential equations with an arbitrary distribution of dispersal times between patches. By identifying steady states and analyzing local stability, conditions for competitive exclusion, coexistence or extinction are determined in terms of the system parameters. These are confirmed by numerical simulations with a delta function distribution, showing that all solutions approach a steady state and that high dispersal is generally a disadvantage to a species. However, if the two species have identical local dynamics, then small dispersal rates (with certain parameter restrictions) can be an advantage to the dispersing species. If the number of species is increased to three, then oscillatory coexistence with dispersal delay is possible.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.283coexistencedispersal delaycompetitionpatch modelstability. |
| spellingShingle | Nancy Azer P. van den Driessche Competition and Dispersal Delays in Patchy Environments Mathematical Biosciences and Engineering coexistence dispersal delay competition patch model stability. |
| title | Competition and Dispersal Delays in Patchy Environments |
| title_full | Competition and Dispersal Delays in Patchy Environments |
| title_fullStr | Competition and Dispersal Delays in Patchy Environments |
| title_full_unstemmed | Competition and Dispersal Delays in Patchy Environments |
| title_short | Competition and Dispersal Delays in Patchy Environments |
| title_sort | competition and dispersal delays in patchy environments |
| topic | coexistence dispersal delay competition patch model stability. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.283 |
| work_keys_str_mv | AT nancyazer competitionanddispersaldelaysinpatchyenvironments AT pvandendriessche competitionanddispersaldelaysinpatchyenvironments |