Dynamical analysis of a delayed diffusive predator–prey model incorporating hyperbolic mortality and fear effect

In this paper, we consider a delayed diffusive predator–prey model incorporating hyperbolic mortality and fear effect. It is shown that the model undergoes Hopf bifurcation as the maturity time delay cross the threshold value, and Turing bifurcation occurs as the diffusion coefficient ratio between prey and predator is small. The study indicates that increasing predator’s mortality can increase the number of prey, but it does not benefit to the coexistence and stability of predator and prey. The increase of fear effect has a positive effect on the population size.