Mediated Remote Synchronization of Kuramoto-Sakaguchi Oscillators: The Number of Mediators Matters

Cortical regions without direct neuronal connections have been observed to exhibit synchronized dynamics. A recent empirical study has further revealed that such regions that share more common neighbors are more likely to behave coherently. To analytically investigate the underlying mechanisms, we consider that a set of $n$ oscillators, which have no direct connections, are linked through $m$ intermediate oscillators (called mediators ), forming a complete bipartite network structure. Modeling the oscillators by the Kuramoto-Sakaguchi model, we rigorously prove that mediated remote synchronization , i.e., synchronization between those $n$ oscillators that are not directly connected, becomes more robust as the number of mediators increases. Simulations are also carried out to show that our theoretical findings can be applied to other general and complex networks.