Spatial patterns created by cross-diffusion for a three-species food chain model

Abstract

This paper deals with the stability analysis to a three-species food chain model with cross-diffusion, the results of which show that there is no Turing instability but cross-diffusion makes the model instability possible. We then show that the spatial patterns are spotted patterns by using numerical simulations. In order to understand why the spatial patterns happen, the existence of the nonhomogeneous steady states is investigated. Finally, using the Leray–Schauder theory, we demonstrate that cross-diffusion creates nonhomogeneous stationary patterns.