Abstract
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.
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