Note on a ratio-dependent predator–prey system with diffusion

Pang and Wang (Proc. Roy. Soc. Edinburg A 133 (4) (2003) 919) studied a ratio-dependent predator–prey model with diffusion subject to the homogeneous Neumann boundary condition and gave some qualitative descriptions of solutions to this reaction–diffusion system and its corresponding steady-state problem. In the present paper, we derive some further results for this model, that is, we discuss the global stability of the unique constant positive steady-state, give improved a priori estimates for positive steady-states and thus obtain some improved non-existence results for non-constant positive steady-states.