Spatiotemporal dynamics of a predator-prey model with a gestation delay and nonlocal competition

Predator gestation delay and nonlocal competition play key roles in controlling population density and maintaining ecosystem stability. In order to control the Dendrolimus superans that cause serious damage to forests, we propose a predator-prey reaction-diffusion equation with Holling type-II functional response function, gestation delay, and nonlocal competition. We investigated the existence conditions of the Hopf bifurcation and obtained its normal form of Hopf bifurcation by employing the multiple time scales method. We selected the appropriate parameters for numerical simulation and found that the gestation delay is helpful to maintain the stability of the population density of Dendrolimus superans.