A Spectral Approach to Synchronizability of Interdependent Networks

Abstract

The quality of life in full developed countries depends on the cooperative functioning of different infrastructures. One of the most striking problems is to understand in simple terms to what extent this cooperation can be assured. The complexity science provides a powerful means to analyze the interaction of such critical infrastructures at pure topological level. The application of the paradigm of complexity to the global system resulting from the interdependent infrastructures leads to the concept of “Network of Networks”. The present work is devoted to understand emergent (that is collective) synchronization behaviors through the spectral analysis of the laplacian. We provide evidence that, upon increasing the number of links between the different infrastructures, the behavior of the total system experiences a drastic changes in its synchronization modes. When few links are introduced, the synchronization inside the component networks is very fast and the global synchronization takes place mainly at the boundaries; on the other side, when the number of links exceeds a threshold, the bottlenecks for the synchronization process localize mainly inside the component networks.