Higher-Order Interactions in the Network of Erbium-Doped Fiber Lasers

The dynamics and synchronization properties of a network of three erbium-doped fiber lasers coupled via higher-order interactions (HOI) are investigated using simplicial complexes. Three coupling configurations are analyzed: first-order only, second-order only, and their combination. Several synchronization metrics, including the average synchronization error, similarity index, and correlation coefficient, are employed to characterize the effects of HOI. The results demonstrate that incorporating second-order coupling substantially enriches the system’s dynamical behavior, revealing a greater diversity of collective states than first-order coupling alone. While complete synchronization is not achieved within the bounded coupling strengths considered, both phase synchronization and anticipation synchronization emerge within distinct parameter intervals.