Non-triangular cross-diffusion systems with predator–prey reaction terms

Abstract

A predator–prey system involving cross-diffusion is obtained at the formal level as a singular limit of a four-species reaction–diffusion system, following the approach proposed in the context of ODEs by Geritz and Gyllenberg (J Theor Biol 314:106–108, 2012). Part of this derivation can be made rigorous. The possibility of appearance of Turing patterns for this cross-diffusion system is studied, and compared to what happens when standard diffusion terms replace the cross-diffusion terms.