Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit

We rigorously prove the passage from a Lotka-Volterra reaction-diffusion system towards a cross-diffusion system at the fast reaction limit. The system models a competition of two species, where one species has a more diverse diet than the other. The resulting limit gives a cross-diffusion system of...

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Bibliographic Details
Published inJournal of mathematical biology Vol. 83; no. 5; p. 58
Main Authors Brocchieri, Elisabetta, Corrias, Lucilla, Dietert, Helge, Kim, Yong-Jung
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2021
Springer Nature B.V
Springer
Subjects
Analysis of PDEs
Applications of Mathematics
Boundary conditions
Competition
Diet
Diffusion
Diffusion rate
Evolution
Mathematical and Computational Biology
Mathematical models
Mathematics
Mathematics and Statistics
Population
Cross-diffusion
Entropy
Primary : 35B25, 35B40, 35K57, 35Q92, 92D25
Secondary 35B45, 35K45
Turing instability
Starvation-driven diffusion
starvation-driven diffusion
entropy
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Summary:We rigorously prove the passage from a Lotka-Volterra reaction-diffusion system towards a cross-diffusion system at the fast reaction limit. The system models a competition of two species, where one species has a more diverse diet than the other. The resulting limit gives a cross-diffusion system of a starvation driven type. We investigate the linear stability of homogeneous equilibria of those systems and rule out the possibility of cross-diffusion induced instability (Turing instability). Numerical simulations are included which are compatible with the theoretical results.
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ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-021-01679-y