Positive steady states of a diffusive predator–prey system with modified Holling–Tanner functional response☆

By Hongbo Shi, Wan-Tong Li, Guo Lin. 2010

74 citations recorded by the source corpus.

In this paper, we study a diffusive predator–prey system with modified Holling–Tanner functional response under homogeneous Neumann boundary condition. The qualitative properties, including the global attractor, persistence property, 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.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/1c54b51883e4812d2507a1dbc2d1a7f391f43efa

Citations in the corpus

• Existence and non-existence of spatial patterns in a ratio-dependent predator–prey model (2015, unknown): “…criteria for the stability of homogeneous steady-state and derivation of appropriate conditions for the existence and/or non-existence of non-constant stationary states (Pang and Wang, 2003; Peng and Shi, 2009; Peng et al., 2008; Shi, 2002; Shi et al., 2010; Smoller, 1994; Wang et al., 2011).”