Pattern dynamics analysis of a space-time discrete spruce budworm model

In view of the living habits of the spruce budworm, a space-time discrete model with periodic boundary conditions is established. Through the analysis of the effect of diffusion, rich dynamic properties are obtained, such as chaotic phenomena, stable spatially homogeneous states, pure Turing instability, spatially homogeneous periodic oscillations, and Flip-Turing instability. These findings hold significant biological significance and offer valuable insights for research in ecosystem stability study, pest control strategies, as well as evolution and adaptation studies. In addition, the relationship between complex patterns and biological mechanisms is discussed. The results in this paper can help people better understand the biological significance of controlling the spruce budworm.