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.
Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit / Brocchieri, Elisabetta; Corrias, Lucilla; Dietert, Helge; Kim, Yong-Jung. - In: JOURNAL OF MATHEMATICAL BIOLOGY. - ISSN 0303-6812. - (2020).
Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit
Elisabetta Brocchieri;
2020
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.