Impacts of nonlocal fear effect and delay on a reaction–diffusion predator–prey model

Abstract

In this research, we examine a predator–prey model in which nonlocal fear plays a role alongside delay in a reaction–diffusion framework. We integrate two delays into the model to account for the lag between when fear starts affecting the growth rate of prey and when it starts affecting the growth rate of the predator through feedback. The first step is to investigate local and global stability and bifurcations in the equilibrium states of the nondelayed model. We explore the Hopf bifurcation in the delayed model using the delay as the bifurcation parameter. Our theoretical findings are then backed up by certain simulations. It reveals how the system, depending on its level of anxiety and the time delays involved, displays a wide range of spatiotemporal patterns.