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Strategy and stationary pattern in a three-species predator–prey model. (English) Zbl 1106.35016

The authors indicate that, in all the predator-prey models with cross diffusion studied so far, stationary patterns arise already with the introduction of the diffusion term for each species. The model being studied in this paper seems to be the first where stationary patterns do not emerge from the diffusion of individual species, but only appear with the introduction of cross diffusion.

MSC:

35J55 Systems of elliptic equations, boundary value problems (MSC2000)
92D25 Population dynamics (general)
35B41 Attractors
35J60 Nonlinear elliptic equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)

Keywords:

cross diffusion
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