Spatial Pattern Formation in Host–Parasitoid Model of Massicus raddei Infestation with Fear Effect and Nonlocal Competition

In this paper, we construct a delayed host–parasitoid model with homogeneous Neumann boundary condition, incorporating fear effect and nonlocal competition, to investigate the biological control of Massicus raddei. Through linear stability and eigenvalue analysis, we derive the conditions for Turing, Hopf, and Turing–Hopf bifurcations. Theoretically, the multiple time scales method is employed to derive the normal form of this codimension-2 bifurcation. By conducting systematic analysis and numerical simulations with biologically meaningful parameters, we discover an interesting phenomenon that the dynamics of the system are closely related to the domain size. For large domains, the system can undergo Hopf–pitchfork bifurcation, exhibiting spatially homogeneous steady states, spatially inhomogeneous steady states, and spatially inhomogeneous periodic solutions. Numerical simulations further demonstrate that increasing the diffusion coefficient of the parasitoid can significantly enhance the biocontrol efficacy against M. raddei. However, when the domain size is reduced under the same parameter set, the system may undergo degenerate Hopf–transcritical bifurcation. Moreover, further reducing the pregnancy delay and the diffusion coefficient of the parasitoid can induce stable quasi-periodic solutions, a phenomenon not observed in large domains. Accordingly, these findings provide an important theoretical basis for designing biological control strategies against M. raddei tailored to different spatial scales.