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Synchronization of non-identical oscillators coupled through complex networksis an important example of collective behavior. It is interesting to ask howthe structural organization of network interactions influences this process.Several studies have uncovered optimal topologies for synchronization by makingpurposeful alterations to a network. Yet, the connectivity patterns of manynatural systems are often not static, but are rather modulated over timeaccording to their dynamics. This co-evolution - and the extent to which thedynamics of the individual units can shape the organization of the networkitself - is not well understood. Here, we study initially randomly connectedbut locally adaptive networks of Kuramoto oscillators. The system employs aco-evolutionary rewiring strategy that depends only on instantaneous, pairwisephase differences of neighboring oscillators, and that conserves the totalnumber of edges, allowing the effects of local reorganization to be isolated.We find that a simple regulatory rule - which preserves connections betweenmore out-of-phase oscillators while rewiring connections between more in-phaseoscillators - can cause initially disordered networks to organize into morestructured topologies that support enhanced synchronization dynamics. Weexamine how this process unfolds over time, finding both a dependence on theintrinsic frequencies of the oscillators and the global coupling. For largeenough coupling and after sufficient adaptation, the resulting networks exhibitdegree - frequency and frequency - neighbor frequency correlations. Theseproperties have previously been associated with optimal synchronization orexplosive transitions. By considering a time-dependent interplay betweenstructure and dynamics, this work offers a mechanism through which emergentphenomena can arise in complex systems utilizing local rules.

Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators