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Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit.
J Math Biol
; 83(5): 58, 2021 11 03.
Artículo
en Inglés
| MEDLINE
| ID: mdl-34731313
RESUMEN
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.