Complex Spatiotemporal Patterns of Pine and Monochamus Alternatus Model Induced by Cross-Diffusion and Convection

Source abstract

Based on the two-dimensional reaction–diffusion model, the spatiotemporal dynamical characteristics of the semi-discrete pine–Monochamus alternatus system with cross-diffusion and convection effect were studied in this work. Firstly, the stability conditions of the equilibrium point were obtained through linear stability analysis and Lyapunov coefficients, as well as the Andronov–Hopf bifurcation, which explained the reason for the periodic outbursts of the Lyapunov population from a dynamic perspective. Subsequently, through the characteristic equations of the Laplace operator ∇2 and the gradient operator ∇, the critical discrimination conditions for the occurrence of Turing instability in the system were obtained and revealed that the phenomenon of frequent damage to pine caused by the pink Monochamus is in the form of patches. Finally, the reliability of the theoretical analysis was verified through numerical simulation, and the dual effect of convection was clearly found in the system. Moderate convection can change the pattern shape, while strong convection produces a “washout effect”, completely inhibiting the formation of the pattern. This indicates that factors such as wind or the directional migration of Monochamus alternatus significantly affect the spatial distribution pattern of pests. Therefore, the theoretical research on Turing instability of models with convection terms may provide inspiration for subsequent studies.