Coexistence of explosive and driven forms of remote synchronization in star networks

Remote synchronization (RS)-the emergence of phase coherence among nonadjacent peripheral nodes while remaining desynchronized from the mediating hub-is a fundamental mechanism for long-range coordination in complex networks. So far all studies have been focusing on only a single RS plateau generated by tuning intrinsic parameters such as coupling strength or time delay. Here we report an unobserved phenomenon: the coexistence of two distinct forms of RS in externally forced star networks. Using coupled Stuart-Landau oscillators, we show that a weak external forcing can induce an abrupt, explosive transition in which the leaf nodes synchronize at an intrinsic, network-selected frequency, yielding an explosive RS state (RS1) that is independent of the forcing frequency. As the forcing amplitude increases, the leaves undergo a second transition and become entrained by the external drive, producing a driven RS state (RS2). This double-RS structure occupies a well-defined region in the forcing-parameter space and depends sensitively on the spatial location of the stimulus. We further develop a simple theoretical framework that links explosive RS1 to a forcing-induced renormalization of the effective coupling and explains RS2 as a hub-assisted entrained RS regime. These results reveal two qualitatively different mechanisms of RS and suggest a mechanistic framework by which external stimuli can sculpt coherent interactions between distant brain areas.