Temporal And Spatial Patterns Of A Diffusive Predator-prey Model With Mutual Interference

In this paper,the temporal and spatial patterns of a diffusive predator-prey model with mutual interference are studied.First,by the linearization method,the local stability of the positive equilibrium is discussed.Next,choosing intrinsic growth rate of predator as the bifur-cation parameter,we obtain the existence of Hopf bifurcation.Furthermore,the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are established by the center manifold theory and the normal form method.Then,we demonstrate that the diffusion-driven Turing instability occurs under suitable conditions.In addition,a priori estimates,the nonexistence and existence of positive non-constant steady-state solutions are studied.Finally,some numerical simulations are shown to verify the analytical results.