Synchronization in complex oscillator networks and smart grids

Florian Dörfler, Michael Chertkov, Francesco Bullo

Research output: Contribution to journalArticlepeer-review

700 Scopus citations


The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A widely adopted model of a coupled oscillator network is characterized by a population of heterogeneous phase oscillators, a graph describing the interaction among them, and diffusive and sinusoidal coupling. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here, we present a unique, concise, and closed-form condition for synchronization of the fully nonlinear, nonequilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters; they are statistically correct for almost all networks; and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks, such as electrical power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex network scenarios and in smart grid applications.

Original languageEnglish (US)
Pages (from-to)2005-2010
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number6
StatePublished - Feb 5 2013
Externally publishedYes


  • Nonlinear dynamics
  • Power grids

ASJC Scopus subject areas

  • General


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