Modeling the fear effect in the predator-prey dynamics with an age structure in the predators

We incorporate the fear effect and the maturation period of predators into a diffusive predator-prey model. Local and global asymptotic stability for constant steady states as well as uniform persistence of the solution are obtained. Under some conditions, we also exclude the existence of spatially nonhomogeneous steady states and the steady state bifurcation bifurcating from the positive constant steady state. Hopf bifurcation analysis is carried out by using the maturation period of predators as a bifurcation parameter, and we show that global Hopf branches are bounded. Finally, we conduct numerical simulations to explore interesting spatial-temporal patterns.