Multivariable coupling and synchronization in complex networks

Abstract

Synchronization in complex networks is an evergreen subject with numerous applications in biological, social, and technological systems. We here study whether a transition from a single variable to multivariable coupling facilitates the emergence of synchronization in a network of circulant oscillators. We show that the network indeed has much better synchronizability when individual dynamical units are coupled through multiple variables rather than through just one. In particular, we consider in detail four different coupling scenarios for a simple three-dimensional chaotic circulant system, and we determine the smallest coupling strength needed for complete synchronization. We find that the smallest coupling strength is needed when the coupling is through all three variables, and that for the same level of synchronization through a single variable a much stronger coupling strength is needed. Our results thus show that multivariable coupling provides a significantly more efficient synchronization profile in complex networks.