Turing pattern formation in a predator-prey system with cross diffusion

The paper explores the impacts of cross-diffusion on the formation of spatial patterns in a ratio-dependent predator-prey system with zero-flux boundary conditions. Our results show that under certain conditions, cross-diffusion can trigger the emergence of spatial patterns which is however impossible under the same conditions when cross-diffusion is absent. We give a rigorous proof that the model has at least one spatially heterogenous steady state by means of the Leray-Schauder degree theory. In addition, numerical simulations are performed to visualize the complex spatial patterns. (C) 2014 Elsevier Inc. All rights reserved.