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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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