Synchronization reveals topological scales in complex networks

We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology and spectral graph analysis.Comment: 4 pages, 3 figure

Synchronization processes in complex networks

We present an extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks. In the synchronization process, different structures corresponding to well defined communities of nodes appear in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology and spectral graph analysis.Comment: 16 pages, 4 figures. To appear in Physica D "Special Issue on dynamics on complex networks

Synchronizabilities of Networks: A New index

The random matrix theory is used to bridge the network structures and the dynamical processes defined on them. We propose a possible dynamical mechanism for the enhancement effect of network structures on synchronization processes, based upon which a dynamic-based index of the synchronizability is introduced in the present paper.Comment: 4pages, 2figure

Epidemics and chaotic synchronization in recombining monogamous populations

We analyze the critical transitions (a) to endemic states in an SIS epidemiological model, and (b) to full synchronization in an ensemble of coupled chaotic maps, on networks where, at any given time, each node is connected to just one neighbour. In these "monogamous" populations, the lack of connectivity in the instantaneous interaction pattern -that would prevent both the propagation of an infection and the collective entrainment into synchronization- is compensated by occasional random reconnections which recombine interacting couples by exchanging their partners. The transitions to endemic states and to synchronization are recovered if the recombination rate is sufficiently large, thus giving rise to a bifurcation as this rate varies. We study this new critical phenomenon both analytically and numerically

Multiple dynamical time-scales in networks with hierarchically nested modular organization

Many natural and engineered complex networks have intricate mesoscopic organization, e.g., the clustering of the constituent nodes into several communities or modules. Often, such modularity is manifested at several different hierarchical levels, where the clusters defined at one level appear as elementary entities at the next higher level. Using a simple model of a hierarchical modular network, we show that such a topological structure gives rise to characteristic time-scale separation between dynamics occurring at different levels of the hierarchy. This generalizes our earlier result for simple modular networks, where fast intra-modular and slow inter-modular processes were clearly distinguished. Investigating the process of synchronization of oscillators in a hierarchical modular network, we show the existence of as many distinct time-scales as there are hierarchical levels in the system. This suggests a possible functional role of such mesoscopic organization principle in natural systems, viz., in the dynamical separation of events occurring at different spatial scales.Comment: 10 pages, 4 figure