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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:

35K51 Initial-boundary value problems for second-order parabolic systems
35K58 Semilinear parabolic equations
92D25 Population dynamics (general)
35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
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