Dynamics analysis of a diffusive predator-prey model with spatial memory and nonlocal fear effect

In this study, we analyze a delayed diffusive predator-prey model with spatial memory and a nonlocal fear effect, taking into account the fact that the effect of fear on the growth rate of prey is delayed. First, we verify the existence and boundedness of the solution of the proposed model. Then all steady states are considered, and the conditions under which they are stable are analyzed in light of the model parameters. For the non-delayed model, local/global stability and bifurcations are studied at constant steady states. For the delayed model, we use the delay as the bifurcation parameter to study the Hopf bifurcation and Turing-Hopf bifurcation. Finally, numerical simulations are presented to validate our theoretical findings. It demonstrates that the system exhibits a variety of spatiotemporal patterns as a result of spatial memory delay and nonlocal fear effect delay.