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Zbl 1202.35116
Shi, Hong-Bo; Li, Wan-Tong; Lin, Guo
Positive steady states of a diffusive predator-prey system with modified Holling-Tanner functional response. (English)
[J] Nonlinear Anal., Real World Appl. 11, No. 5, 3711-3721 (2010). ISSN 1468-1218

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 2000:: *35K51
35K58
92D25 Population dynamics
35B40 Asymptotic behavior of solutions of PDE
35B41 Attractors

Keywords: homogeneous Neumann boundary condition; persistence property; local and global asymptotic stability; large diffusivity

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Zentralblatt MATH Berlin [Germany]