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

AMS Sub ject Classification:

• 35K57
• 35R20
• 92D25