Effect of cross-diffusion on the stationary problem of a predator–prey system with a protection zone

Abstract

This paper is concerned with the steady state problem of a predator–prey cross-diffusion system with herd effect, Allee effect and a protection zone. Some sufficient conditions for the existence of positive steady state solutions are given. Our proof is based on the local and global bifurcation theory and some a priori estimates. Some limiting behavior of positive steady states with respect to the Allee effect constant (α) or the diffusion coefficient (d), are discussed.