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Positive steady states of a diffusive predator-prey system with modified Holling-Tanner functional response. (English) Zbl 1202.35116
Summary: We study a diffusive predator-prey system with modified Holling-Tanner functional response under homogeneous Neumann boundary condition. Qualitative properties, including the global attractor, the persistence property, the local and global asymptotic stability of the unique positive constant equilibrium, are obtained. We also establish the existence and nonexistence of nonconstant positive steady states of this reaction-diffusion system which indicates the effect of large diffusivity.

MSC:
35K51Second-order parabolic systems, initial bondary value problems
35K58Semilinear parabolic equations
92D25Population dynamics (general)
35B40Asymptotic behavior of solutions of PDE
35B41Attractors (PDE)