Dynamics of a threshold-controlled reaction–diffusion pest management model with nonlocal competition and pest refuge

Pest populations are strongly affected by spatial interactions and protected habitats, where nonlocal competition among individuals and pest refuges may alter population persistence and the effectiveness of control strategies. In this paper, we study a threshold-controlled reaction–diffusion pest management model incorporating nonlocal competition and pest refuge effects to investigate their impacts on pest dynamics. Stability and bifurcation analysis reveal that the stability region of the regular equilibrium is determined by both the Hopf bifurcation curves and the Turing bifurcation curves. Additionally, the study of sliding mode dynamics reveals that the boundary of the sliding segment fluctuates over time due to the presence of the nonlocal competition term. Numerical simulations further verify the theoretical analysis, showing that spatially inhomogeneous steady states and periodic solutions result in points across the entire spatial domain not undergoing sliding bifurcation simultaneously. The results provide theoretical insights into how spatial interactions and refuge effects should be considered in designing effective pest management strategies.