Synchronization and 1/f signals in interacting small-world networks

We investigated the synchronization and temporal correlations in a simple signaling network model. The model, which is able to display spatio-temporal avalanches and diverse fractal time correlations, consists of Boolean units located in a small-world network. We evaluated the synchrony between pairs of sets of units by means of the global lability synchronization measure, which is based on the probability of change of the total number of synchronized signals, for a range of evolutions of the system with different correlation dynamics. Here, we show that the global lability distribution exhibits power-law scaling for large-scale dynamics identified with 1/f signals, whereas a breakdown in the scaling behavior emerges when there are deviations toward either short-term correlated or uncorrelated dynamics. Furthermore, we extend our study to interacting multilayer networks, which consist of two small-world networks with different correlation dynamics in each layer. We evaluated the change in the correlation and the synchronization dynamics displayed by the system in terms of the coupling parameter between layers. Our results show that long-range correlated fluctuations naturally emerge or are still present even when coupled layers initially display different correlation dynamics. Moreover, the correlation-synchronization between pairs of global lability events closely follows a power-law scaling when networks are coupled, indicating that there exists a high correlation over long time scales due to information transmission.