Spatiotemporal dynamics of a delayed diffusive ratio-dependent predator-prey model with fear effect

By considering that there is a delay on the impact of fear to the growth rate of prey, we consider a delayed diffusive predator-prey model with fear effect. First, we give some conditions of the existence of the equilibria. Then, sufficient conditions for the occurrence of Turing, Hopf and Turing-Hopf bifurcation are also obtained. Furthermore, the global asymptotic stability of the positive equilibrium is studied. Finally, some numerical simulations are presented to verify our theoretical results. It shows that the system has various spatiotemporal patterns induced by delay.