Stationary patterns of a ratio-dependent predator-prey system with cross-diffusion

Abstract

This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross-diffusion in a bounded domain with no flux boundary condition. We establish the existence and non-existence of non-constant positive steady states (patterns). In particular, we show that under certain hypotheses, the cross-diffusion can create stationary patterns even though the corresponding model without cross-diffusion fails.

Keywords

• existence
• predator-prey system
• cross-diffusion
• positive steady state
• ratiodependence