Modeling spatial adaptation of populations by a time non-local convection cross-diffusion evolution problem |
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Authors: | Gonzalo Galiano |
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Institution: | Dpto. de Matemáticas, Universidad de Oviedo, c/ Calvo Sotelo, 33007 Oviedo, Spain |
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Abstract: | In 19], Sighesada et al. 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 is included. In this article, we introduce a modification of their convective term to take account for the notion of spatial adaptation of populations. After describing the model we briefly discuss its well-possedness and propose a numerical discretization in terms of a mass-preserving time semi-implicit finite differences scheme. Finally, we provide the results of two biologically inspired numerical experiments showing qualitative differences between the original model of 19] and the model proposed in this article. |
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Keywords: | Population dynamics Evolution problem Cross-diffusion Time non-local convection Finite differences Spatial adaptation Segregation |
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