Synchronization in small-world systems

Abstract

An attempt was made to link explicitly the small world (SW) addition of random shortcuts to the synchronization of networks of coupled dynamical systems. A generic formulation that allows to factor out the connectivity content, and thus identify the synchronization threshold with an algebraic property of the Laplacian matrix of the graph was applied. Numerical and analytical study was performed to quantify how the SW scheme improves the synchronizability of the network. Overall, evidence was obtained that the small-world property does not guarantee in general that a network will be synchronizable.