Remote synchronization induced by external signals in star networks

Remote synchronization (RS) is an emerging focus in nonlinear dynamics and complex networks, as it provides insights into how functional connections in the brain arise from its structural network. While previous studies have extensively explored RS under intrinsic coupling conditions, the combined influence of external stimuli and coupling strength, a critical factor in real-world systems, remains unexplored. In this study, we investigate RS in a star network of coupled Stuart–Landau oscillators, a simplified model of hierarchical brain structures, under varying external stimuli and coupling strengths. Using numerical simulations and theoretical analysis, we identify two distinct mechanisms driving RS: direct resonance between external stimuli and leaf nodes, and hub-mediated synchronization facilitated by resonance between the hub node and the stimuli. We further reveal that RS occurs within specific coupling strength ranges and is maximized when the stimulus frequency aligns with the natural frequencies of either the hub or leaf nodes. These results emphasize the delicate interplay between coupling strength and external perturbations in shaping RS, providing a theoretical framework for understanding the mechanisms of RS emergence under external stimuli.