Network specialization: A topological mechanism for the emergence of cluster synchronization

Abstract

Real-world networks are dynamic in that both the state of the network components and the structure of the network (topology) change over time. Most studies regarding network evolution consider either one or the other of these types of network processes. Here we consider the interplay of the two, specifically, we consider how changes in network structure effect the dynamics of the network components. To model the growth of a network we use the specialization model known to produce many of the well-known features observed in real-world networks. We show that specialization results in a nontrivial equitable partition of the network where the elements of the partition form clusters that have synchronous dynamics. We also show that these synchronizing clusters inherit their ability to either locally or globally synchronize from the subnetwork from which they are specialized. To the best of the authors’ knowledge this may be the first example of a topological mechanism that induces spontaneous synchronization and real-world like growth. Thus, network specialization can be used to model the co-evolution of dynamic and topological features found in real-world systems.