Qualitative Analysis on a Reaction-Diffusion Prey-Predator Model and the Corresponding Steady-States - Bie, Qunyi; Peng, Rui (Chinese annals of mathematics. Serie B, 2009)
The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem. The local and global stability of the positive constant steady-state are discussed, and then some results for nonexistence of positive non-constant steady-states are derived.