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Effect of cross-diffusion on the stationary problem of a predator-prey system with a protection zone. (English) Zbl 1442.92144
Summary: This paper is concerned with the steady state problem of a predator-prey cross-diffusion system with herd effect, Allee effect and a protection zone. Some sufficient conditions for the existence of positive steady state solutions are given. Our proof is based on the local and global bifurcation theory and some a priori estimates. Some limiting behavior of positive steady states with respect to the Allee effect constant $$(\alpha)$$ or the diffusion coefficient $$(d)$$, are discussed.
##### MSC:
 92D25 Population dynamics (general) 35K51 Initial-boundary value problems for second-order parabolic systems
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