Abstract
This paper is devoted to study a general diffusive predator-prey system with strong Allee effect in the prey. A priori estimate and nonexistence of nonconstant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation. The Hopf bifurcation and steady-state bifurcation from the positive constant solution branch are investigated. These results provide theoretical evidences to the complex spatiotemporal dynamics found by numerical simulations.
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