4.7 Article

Synchronization in complex networks of phase oscillators: A survey

Journal

AUTOMATICA
Volume 50, Issue 6, Pages 1539-1564

Publisher

PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2014.04.012

Keywords

Coupled oscillators; Kuramoto model; Synchronization; Complex networks; Nonlinear analysis

Funding

  1. University of California Los Angeles startup funds
  2. NSF grants [IIS-0904501, CPS-1135819]
  3. Direct For Computer & Info Scie & Enginr [1135819] Funding Source: National Science Foundation
  4. Division Of Computer and Network Systems [1135819] Funding Source: National Science Foundation

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The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research. (C) 2014 Elsevier Ltd. All rights reserved.

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