Spatial heterogeneity localizes Turing patterns in reaction-cross-diffusion systems
Spatial heterogeneity localizes Turing patterns in reaction-cross-diffusion systems
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and reaction terms. Under a suitable asymptotic assumption that the transport is slow over the domain, while gradients in the reaction heterogeneity are …