Spatiotemporal Dynamics in a Time-Delayed <i>Rhizophagus</i> <i>g</i><i>randis</i>-<i>D</i><i>endroctonus </i><i>v</i><i>alens</i> Predator-Prey System with Nonlocal

The objective of this study is to investigate the spatiotemporal dynamics of a Rhizophagus grandis-Dendroctonus valens predator-prey system. Under Neumann boundary conditions, we establish a reaction-diffusion system incorporating Holling-II functional response, nonlocal effect, predator-prey taxis and time delay to elucidate the regulatory mechanisms of chemotactic behaviors and delayed predation pressure on ecosystem stability. In addition, we investigate the existence conditions for Hopf bifurcation and employ the multiple time scales method to derive its normal form. Under appropriate parameter constraints, numerical simulations demonstrate that the system exclusively exhibits Hopf bifurcation in the current parameter configuration, where nonlocal interactions, taxis and time delays synergistically induce the formation of spatially heterogeneous periodic solutions. These results elucidate the intrinsic mechanism underlying periodic pest outbreaks and provide a theoretical foundation for optimizing biological control strategies. Notably, our analysis reveals the critical role of predator taxis capability and delayed predation feedback in stabilizing pest population cycles, offering practical guidance for sustainable forest pest management.