A strongly coupled predator–prey system with non-monotonic functional response

Abstract

The predator–prey system with non-monotonic functional response is an interesting field of theoretical study. In this paper we consider a strongly coupled partial differential equation model with a non-monotonic functional response—a Holling type-IV function in a bounded domain with no flux boundary condition. We prove a number of existence and non-existence results concerning non-constant steady states (patterns) of the underlying system. In particular, we demonstrate that cross-diffusion can create patterns when the corresponding model without cross-diffusion fails.