Synchronization in complex oscillator networks and smart grids
Top Cited Papers
- 14 January 2013
- journal article
- research article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 110 (6), 2005-2010
- https://doi.org/10.1073/pnas.1212134110
Abstract
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.Keywords
This publication has 39 references indexed in Scilit:
- Emergent behaviour of a generalized Viscek-type flocking modelNonlinearity, 2010
- Synchronization in symmetric bipolar population networksPhysical Review E, 2009
- Synchronization in complex networksPhysics Reports, 2008
- Paths to Synchronization on Complex NetworksPhysical Review Letters, 2007
- Complex networks: Structure and dynamicsPhysics Reports, 2006
- Heterogeneity in Oscillator Networks: Are Smaller Worlds Easier to Synchronize?Physical Review Letters, 2003
- Huygens's clocksProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2002
- Observations on the geometry of saddle node bifurcation and voltage collapse in electrical power systemsIEEE Transactions on Circuits and Systems I: Regular Papers, 1992
- Quasientrainment and slow relaxation in a population of oscillators with random and frustrated interactionsPhysical Review Letters, 1992
- Steady-State Security Regions of Power SystemsIEEE Transactions on Circuits and Systems, 1982