In this study,we consider a diffusive predator-prey model with multiple Allee effects induced by fear factors.We investigate the existence,boundedness and permanence of the solution of the system.We also discuss the existence and non-existence of non-constant solutions.We derive sufficient conditions for spatially homogeneous(non-homogenous)Hopf bifurcation and steady state bifurcation.Theoretical and numerical simulations show that strong Allee effect and fear effect have great effect on the dynamics of system.
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