Spatiotemporal Dynamics of a Memory-Diffusion Predator-Prey System with Two Delays and Nonlocal Competition

Abstract

Predator gestation delay and memory period, along with nonlocal competition, play key roles in controlling population density and maintaining the stability of ecosystems. To control the population density of the Dendrolimus superans, which causes significant damage to forests, we propose a pest control system incorporating both two delays and nonlocal competition considering Holling II type functional response. We analyze the conditions for the existence of Hopf bifurcation and derive the normal form of Hopf bifurcation using multiple time scales method. Considering the biological significance, we employ appropriate parameters for numerical simulations. Furthermore, we find that varying habitat complexity parameters leads to different moduli of bifurcation periodic solutions. Especially, both two delays contribute to maintaining the stability of steady states.