Stationary patterns of strongly coupled prey–predator models ✩

We study some elliptic systems arising from 3-component predator–prey models, where crossdiffusions are included in such a way that predator chases the prey and the prey runs away from the predator.We establish the existence and non-existence of non-constant positive solutions. Our results show that the cross-diffusions can create the stationary patterns.  2004 Elsevier Inc. All rights reserved