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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:
92D40Ecology
35K57Reaction-diffusion equations
35B35Stability of solutions of PDE
35B40Asymptotic behavior of solutions of PDE
35B32Bifurcation (PDE)
35J55Systems of elliptic equations, boundary value problems (MSC2000)