Modular synchronization in complex networks

Abstract

We study the synchronization transition (ST) of a modified Kuramoto model on two different types of modular complex networks. It is found that the ST depends on the type of intermodular connections. For the network with decentralized (centralized) intermodular connections, the ST occurs at finite coupling constant (behaves abnormally). Such distinct features are found in the yeast protein interaction network and the Internet, respectively. Moreover, by applying the finite-size scaling analysis to an artificial network with decentralized intermodular connections, we obtain the exponent associated with the order parameter of the ST to be beta approximately 1 different from beta(MF) approximately 1/2 obtained from the scale-free network with the same degree distribution but the absence of modular structure, corresponding to the mean field value.

Topological complexity of frictional interfaces: friction networks

“…In our case study, it follows that information propagation (entrapping of energy) through profiles is faster in perpendicular profiles than in parallel ones; the rate of energy storage is controlled with perpendicular patterns of contact patches. Here, one may assume that the flux of energy is storied over the networks, while the topology of the networks is invariant during the entrapping or deformation process Depending on the network structure, the synchronization time (time until a steady state is reached) will be different (Arenas et al, 2008;Oh et al, 2005). One may infer that the trapping of energy in pre-peak stages is faster than in post-peak stages.…”

Effects of the network structural properties on its controllability

“…Synchronizability and synchronization dynamics of networks characterized by community structure have been previously studied in [28,29,30]. In [28], the interplay between modular synchronization and global synchronization has been discussed for networks affected by community structure.…”

“…In [28], the interplay between modular synchronization and global synchronization has been discussed for networks affected by community structure. In [29], the dynamic time scales of hierarchical synchronization among network communities have been studied, and a connection between the spectral information of the whole Laplacian spectrum and the dynamical process of modular synchronization has been reported.…”

Synchronization processes in complex networks

“…In this context the interest concerns not the final locked state in itself but the route to the attractor. In particular, it has been shown [33,34] that high densely interconnected sets of oscillators (motifs) synchronize more easily that those with sparse connections. This scenario suggests that for a complex network with a non-trivial connectivity pattern, starting from random initial conditions, those highly interconnected units forming local clusters will synchronize first and then, in a sequential process, larger and larger spatial structures also will do it up to the final state where the whole population should have the same phase.…”