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

Abstract : 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 Turing instability. Numerical simulations are included which are compatible with the theoretical results.
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https://hal.archives-ouvertes.fr/hal-03013229
Contributor : Helge Dietert <>
Submitted on : Thursday, November 19, 2020 - 10:41:48 AM
Last modification on : Friday, April 16, 2021 - 3:31:26 AM
Long-term archiving on: : Saturday, February 20, 2021 - 6:18:29 PM

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  • HAL Id : hal-03013229, version 1
  • ARXIV : 2011.10304

Citation

Elisabetta Brocchieri, Lucilla Corrias, Helge Dietert, Yong-Jung Kim. Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit. 2020. ⟨hal-03013229⟩

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