Pattern formation in a prey-predator system with finite interaction length and space-dependent diffusivity in confined environments

We study a prey-predator system with heterogeneous diffusivities and nonlinear kinetics that depend on the species interaction lengths. These systems exhibit spatial patterns via the Turing instability mechanism driven either by constant diffusion coefficients or by the characteristic interaction lengths. Position-dependent diffusivities can occur in the effective approach to narrow channels but also in fractal geometries, where it is well-known that a power-law diffusivity can model medium heterogeneities leading to anomalous diffusion. We find that, in this case, the dispersion relation mixes the characteristic length with the anomalous exponent of the diffusion coefficient. (author)