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Stationary patterns of the stage-structured predator-prey model with diffusion and cross-diffusion. (English) Zbl 1228.35258

Summary: 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.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D25 Population dynamics (general)
35K57 Reaction-diffusion equations
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