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Stationary patterns caused by cross-diffusion for a three-species prey-predator model. (English) Zbl 1121.92069

Summary: We study a system arising from a three-component prey-predator model with prey- dependent and ratio-dependent functional responses, where cross-diffusion is included in such a way that the predator chases the prey and the prey runs away from the predator. We prove that cross-diffusion can generate stationary patterns (nonconstant positive steady states).

MSC:

92D40 Ecology
35K57 Reaction-diffusion equations
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B32 Bifurcations in context of PDEs
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
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