Bifurcation and spatio-temporal patterns in a diffusive predator-prey system

A diffusive predator-prey system with predator functional response subject to Neumann boundary conditions is considered. Existence, nonexistence, and boundedness of non-constant 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.