Dynamics in a diffusive predator-prey system with ratio-dependent predator influence

A diffusive predator-prey system with predator functional response subject to Neumann boundary conditions is considered. Existence, nonexistence, and boundedness of positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation. Hopf and steady-state bifurcation analyses are carried out in detail. These results provide theoretical evidences to the complex spatio-temporal dynamics found by numerical simulation.