Synchronization in complex networks

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Abstract

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.

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Emergence of scaling in random networks

Reka Albert, Albert-László Barabási (2000)

Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature is found to be a consequence of the two generic mechanisms that networks expand continuously by the addition of new vertices, and new vertices attach preferentially to already well connected sites. A model based on these two ingredients reproduces the observed stationary scale-free distributions, indicating that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

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The structure and function of complex networks

M. Newman (2003)

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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Statistical mechanics of complex networks

Reka Albert, Albert-László Barabási (2001)

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.

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Publication date Created: 19 May 2008

Publication date Updated: 2008-12-12

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DOI: 10.1016/j.physrep.2008.09.002

ArXiV ID: 0805.2976

SO-VID: d0027dba-793b-43c1-bf1b-f2c85cc3f649

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http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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Journal reference Physics Reports, Volume 469, Issue 3, December 2008, Pages 93-153

Comments Final version published in Physics Reports. More information available at http://synchronets.googlepages.com/

Synchronization in complex networks

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Most cited references 10

Emergence of scaling in random networks

The structure and function of complex networks

Statistical mechanics of complex networks

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