Information storage and transfer in the synchronization process in locally-connected networks

Synchrony is a phenomenon where a group of weakly interacting oscillators demonstrate the ability of mutual entrainment, organizing themselves to reach a highly ordered state. The study of synchrony has been hindered by the inherent nature of complex systems requiring the system be studied at a global level. To create new insights here, we use information-theoretical techniques to view the synchronization process as a distributed computation, and to measure the information storage and transfer at each node in the system at each time step. These application-independent measures provide results that can be compared to other systems, and also study the local dynamics of synchronization within the system. This has produced novel insights, including that the computation of the synchronized state appears to be completed much more quickly than application-specific measures (such as the order parameter) would indicate. We also found distinct differences in the computational properties of various nodes, allowing us to develop a theory of the computational dynamics of the synchronization process.