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The global bifurcation for a prey-predator model with cross-diffusion and B-D functional response. (Chinese. English summary) Zbl 1374.35053

Summary: This paper concerns the existence of positive solutions for a predator-prey model with cross-diffusion and B-D functional response under homogeneous Dirichlet boundary conditions. By the maximum principle, a priori estimate of positive solutions is obtained. By considering the related eigenvalue problems, two unbounded neutral curves are given. Then by Crandall-Rabinowitz bifurcation theory, the existence of positive solutions to a local bifurcation is proved. Finally, the local bifurcation is developed to the global one.

MSC:

35B32 Bifurcations in context of PDEs
35B09 Positive solutions to PDEs
35B45 A priori estimates in context of PDEs
92D25 Population dynamics (general)
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