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Journal articles

Reduction to a single closed equation for 2 by 2 reaction-diffusion systems of Lotka-Volterra type

Abstract : We consider general models of coupled reaction-diffusion systems for interacting variants of the same species. When the total population becomes large with intensive competition, we prove that the frequencies (i.e. proportions) of the variants can be approached by the solution of a simpler reaction-diffusion system, through a singular limit method and a relative compactness argument. As an example of application, we retrieve the classical bistable equation for Wolbachia's spread into an arthropod population from a system modeling interaction between infected and uninfected individuals.
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https://hal.archives-ouvertes.fr/hal-01264980
Contributor : Nicolas Vauchelet Connect in order to contact the contributor
Submitted on : Tuesday, February 2, 2016 - 10:58:07 PM
Last modification on : Friday, February 4, 2022 - 3:13:24 AM
Long-term archiving on: : Saturday, November 12, 2016 - 4:24:29 AM

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  • HAL Id : hal-01264980, version 2
  • ARXIV : 1602.01058

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Martin Strugarek, Nicolas Vauchelet. Reduction to a single closed equation for 2 by 2 reaction-diffusion systems of Lotka-Volterra type. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2016, 76 (5), pp.2060-2080. ⟨hal-01264980v2⟩

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