期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 110, 期 6, 页码 2005-2010出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1212134110
关键词
nonlinear dynamics; power grids
资金
- National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory [DE C52-06NA25396]
- National Science Foundation [IIS-0904501, CPS-1135819]
- Direct For Computer & Info Scie & Enginr [1135819] Funding Source: National Science Foundation
- Directorate For Engineering
- Div Of Electrical, Commun & Cyber Sys [1128501] Funding Source: National Science Foundation
- Division Of Computer and Network Systems [1135819] Funding Source: National Science Foundation
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.
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