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.

arXiv commentJournal of Mathematical Biology, Springer Verlag (Germany), 2021

References in corpus (5)

• The boundedness-by-entropy principle for cross-diffusion systems
• Global existence analysis of cross-diffusion population systems for multiple species
• Rigorous mean-field limit and cross diffusion
• About the entropic structure of detailed balanced multi-species cross-diffusion equations
• Persisting entropy structure for nonlocal cross-diffusion systems