Qualitative analysis on a cubic predator-prey system with diffusion - Qunyi Bie (Electronic Journal of Qualitative Theory of Differential Equations, 2011)
In this paper, we study a cubic predator-prey model with diffusion. We first establish the global stability of the trivial and nontrivial constant steady states for the reaction diffusion system, and then prove the existence and non-existence results concerning non-constant positive stationary solutions by using topological argument and the energy method, respectively.