Network synchronization: Spectral versus statistical properties

We consider synchronization of weighted networks, possibly with asymmetrical connections. We show that the synchronizability of the networks cannot be directly inferred from their statistical properties. Small local changes in the network structure can sensitively affect the eigenvalues relevant for synchronization, while the gross statistical network properties remain essentially unchanged. Consequently, commonly used statistical properties, including the degree distribution, degree homogeneity, average degree, average distance, degree correlation, and clustering coefficient, can fail to characterize the synchronizability of networks

Enhance synchronizability by structural perturbations

In this paper, we investigate the collective synchronization of system of coupled oscillators on Barab\'{a}si-Albert scale-free network. We propose an approach of structural perturbations aiming at those nodes with maximal betweenness. This method can markedly enhance the network synchronizability, and is easy to be realized. The simulation results show that the eigenratio will sharply decrease to its half when only 0.6% of those hub nodes are under 3-division processes when network size N=2000. In addition, the present study also provides a theoretical evidence that the maximal betweenness plays a main role in network synchronization.Comment: 4 pages, 3 eps figure

Optimization of synchronization in gradient clustered networks

We consider complex clustered networks with a gradient structure, where sizes of the clusters are distributed unevenly. Such networks describe more closely actual networks in biophysical systems and in technological applications than previous models. Theoretical analysis predicts that the network synchronizability can be optimized by the strength of the gradient field but only when the gradient field points from large to small clusters. A remarkable finding is that, if the gradient field is sufficiently strong, synchronizability of the network is mainly determined by the properties of the subnetworks in the two largest clusters. These results are verified by numerical eigenvalue analysis and by direct simulation of synchronization dynamics on coupled-oscillator networks.Comment: PRE, 76, 056113 (2007

Better synchronizability predicted by a new coupling method

In this paper, inspired by the idea that the hub nodes of a highly heterogeneous network are not only the bottlenecks, but also effective controllers in the network synchronizing process, we bring forward an asymmetrical coupling method where the coupling strength of each node depends on its neighbors' degrees. Compared with the uniform coupled method and the recently proposed Motter-Zhou-Kurth method, the synchronizability of scale-free networks can be remarkably enhanced by using the present coupled method.Comment: 6 pages, 6 figures; to be published in EPJ

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com