Lattice Model and Differential Equation Model of Territorial Competition in Cyclic Vegetation Communities

Spatial self-organized patterns are ubiquitous features of vegetation ecosystems, and cyclic nontransitive competition serves as a crucial intrinsic mechanism for sustaining biodiversity. However, existing studies lack cross-scale comparative analyses of vegetation territorial competition based on multiple models. This study combines lattice models and continuous differential equation models to investigate the territorial occupation dynamics and spatial evolution of vegetation communities driven by cyclic competition. The results demonstrate that cyclic competition acts as a core mechanism maintaining vegetation biodiversity, which enables the self-organization of stable spiral wave patterns in space and supports the long-term dynamic coexistence of multiple species. Discrete and continuous models exhibit highly consistent macroscopic dynamical behaviors, which reveal the intrinsic dynamical characteristics of cyclic competitive systems. By integrating microscopic lattice simulation and macroscopic differential equation analysis, this study verifies that spiral waves represent a highly robust species coexistence mode and clarifies the coupled regulatory effects of species richness and stochasticity on system evolution. The findings further deepen the understanding of the complexity of vegetation ecosystems and provide important theoretical references for subsequent theoretical derivation and field observational research on vegetation community competition and evolution.