Finite element approximation of a population spatial adaptation model
In [18], Sighesada, Kawasaki and Teramoto presented a system of partial differential equations for modeling spatial segregation of interacting species. Apart from competitive Lotka-Volterra (reaction) and population pressure (cross-diffusion) terms, a convective term modeling the populations attract...
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AIMS Press
2013-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.637 |
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| author | Gonzalo Galiano Julián Velasco |
| author_facet | Gonzalo Galiano Julián Velasco |
| author_sort | Gonzalo Galiano |
| collection | DOAJ |
| description | In [18], Sighesada, Kawasaki and Teramoto presented a system of partial differential equations for modeling spatial segregation of interacting species. Apart from competitive Lotka-Volterra (reaction) and population pressure (cross-diffusion) terms, a convective term modeling the populations attraction to more favorable environmental regions was included. In this article, we study numerically a modification of their convective term to take account for the notion of spatial adaptation of populations. After describing the model, in which a time non-local drift term is considered, we propose a numerical discretization in terms of a mass-preserving time semi-implicit finite element method. Finally, we provied the results of some biologically inspired numerical experiments showing qualitative differences between the original model of [18] and the model proposed in this article. |
| format | Article |
| id | doaj-art-1f185a3f12e344c5963142eafbe8ace0 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-1f185a3f12e344c5963142eafbe8ace02025-01-24T02:26:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-03-0110363764710.3934/mbe.2013.10.637Finite element approximation of a population spatial adaptation modelGonzalo Galiano0Julián Velasco1Dpto. de Matemáticas, Universidad de Oviedo, c/ Calvo Sotelo, 33007-OviedoDpto. de Matemáticas, Universidad de Oviedo, c/ Calvo Sotelo, 33007-OviedoIn [18], Sighesada, Kawasaki and Teramoto presented a system of partial differential equations for modeling spatial segregation of interacting species. Apart from competitive Lotka-Volterra (reaction) and population pressure (cross-diffusion) terms, a convective term modeling the populations attraction to more favorable environmental regions was included. In this article, we study numerically a modification of their convective term to take account for the notion of spatial adaptation of populations. After describing the model, in which a time non-local drift term is considered, we propose a numerical discretization in terms of a mass-preserving time semi-implicit finite element method. Finally, we provied the results of some biologically inspired numerical experiments showing qualitative differences between the original model of [18] and the model proposed in this article.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.637finite elementpopulation dynamicssegregation.evolution problemspatial adaptationtime non-local convectioncross-diffusion |
| spellingShingle | Gonzalo Galiano Julián Velasco Finite element approximation of a population spatial adaptation model Mathematical Biosciences and Engineering finite element population dynamics segregation. evolution problem spatial adaptation time non-local convection cross-diffusion |
| title | Finite element approximation of a population spatial adaptation model |
| title_full | Finite element approximation of a population spatial adaptation model |
| title_fullStr | Finite element approximation of a population spatial adaptation model |
| title_full_unstemmed | Finite element approximation of a population spatial adaptation model |
| title_short | Finite element approximation of a population spatial adaptation model |
| title_sort | finite element approximation of a population spatial adaptation model |
| topic | finite element population dynamics segregation. evolution problem spatial adaptation time non-local convection cross-diffusion |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.637 |
| work_keys_str_mv | AT gonzalogaliano finiteelementapproximationofapopulationspatialadaptationmodel AT julianvelasco finiteelementapproximationofapopulationspatialadaptationmodel |