Hub induced remote synchronization and desynchronization in complex networks of Kuramoto oscillators

The concept of "remote synchronization" (RS) was introduced in [Phys. Rev. E 85, 026208 (2012)], where synchronization in a star network of Stuart-Landau oscillators was investigated. In the RS regime therein described, the central hub served as a transmitter of information between peripheral nodes, while maintaining independent dynamics that were asynchronous with the rest of the network. One of the key conclusions of that paper was that RS cannot occur in pure phase-oscillator networks. Here, we show that the RS regime can exist in networks of Kuramoto oscillators, and that hub nodes can actively drive remote synchronization even in the presence of a repulsive mean field. We apply this model to study the synchronization dynamics in complex networks endowed with hub-nodes, an ubiquitous feature of many natural networks. We show that a change in the natural frequency of a hub can alone reshape synchronization patterns, and switch from direct to remote synchronization, or to hub-driven desynchronization. We discuss the potential role of this phenomenon in real-world networks, including the Karate-club and brain connectivity networks.

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