Dynamical analysis of a spatial memory prey–predator system with gestation delay and strong Allee effect

In this paper, we formulate a diffusive prey–predator system with strong Allee effect in prey, spatial memory, and gestation delay of predator. Turing instability and Hopf bifurcation are investigated extensively. The system more easily creates Turing patterns, when the predator owns sluggish memory-induced diffusion. If the predator owns rapid memory-induced diffusion, then the system may present abundant dynamics. Predator with long memory displays a spatial nonhomogeneous periodic spread once the system only contains spatial memory delay. Populations are in a homogeneous or nonhomogeneous periodic spread with gestation period. However, under the combined influences of memory delay and gestation delay, the stability switches appear. Strong Allee effect has obvious influences on the system. The positive equilibrium is linearly stable if there is no strong Allee effect; once strong Allee effect is reasonable, it is unstable. But if the Allee effect is huge enough, then two populations can die out. Finally, we investigate the results by numerical simulations, which demonstrate that spatial memory, gestation delay, and strong Allee effect are conductive to the dynamics of the system.