Stationary patterns created by cross-diffusion for the competitor–competitor–mutualist model ✩

In this paper we consider a competitor–competitor–mutualist model with cross-diffusion.We prove some existence and non-existence results concerning non-constant positive steady-states (patterns). In particular, we demonstrate that the cross-diffusion can create patterns when the corresponding model without cross-diffusion fails.  2003 Elsevier Inc. All rights reserved