Asymptotic dynamics and spatial patterns of a ratio-dependent predator–prey system with prey-taxis

This paper is concerned with the global dynamics of a ratio-dependent predator–prey system with prey-taxis. We establish the global existence and uniform-in-time boundedness of solutions in any dimensional bounded domain with Neumann boundary conditions, and furthermore prove the global stability of homogeneous steady states under certain conditions. Finally we perform numerical simulations to show that the pattern formation may arise and prey-taxis is a factor driving the evolution of spatial inhomogeneity into homogeneity.