A qualitative study on general Gause-type predator–prey models with constant diffusion rates

In this paper, we study the qualitative behavior of non-constant positive solutions on a general Gause-type predator–prey model with constant diffusion rates under homogeneous Neumann boundary condition. We show the existence and non-existence of non-constant positive steady-state solutions by the effects of the induced diffusion rates. In addition, we investigate the asymptotic behavior of spatially inhomogeneous solutions, local existence of periodic solutions, and diffusion-driven instability in some eigenmode.