Stationary patterns of the stage-structured predator–prey model with diffusion and cross-diffusion

This paper is concerned with the reaction diffusion version with homogeneous Neumann boundary conditions of a stage-structured predator–prey model. We first show that the nonnegative constant steady states are globally stable, which implies that corresponding elliptic system has no non-constant positive solutions. When we introduce the cross-diffusion, it can be shown that the strongly coupled version has non-constant positive solutions. This shows that the cross-diffusion may cause the existence of non-constant positive steady states.