Dynamics of Cluster Synchronisation in Modular Networks: Implications for Structural and Functional Networks

Abstract

Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional network. A fundamental question in the analysis of complex systems concerns the relation between functional and structural networks. Using synchronisation as a paradigm for network functionality, we study the dynamics of cluster formation in functional networks. We show that the functional network can drastically differ from the structural network. We uncover the mechanism driving these bifurcations by obtaining necessary conditions for modular synchronisation.