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      Spontaneous synchrony in power-grid networks

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          Abstract

          An imperative condition for the functioning of a power-grid network is that its power generators remain synchronized. Disturbances can prompt desynchronization, which is a process that has been involved in large power outages. Here we derive a condition under which the desired synchronous state of a power grid is stable, and use this condition to identify tunable parameters of the generators that are determinants of spontaneous synchronization. Our analysis gives rise to an approach to specify parameter assignments that can enhance synchronization of any given network, which we demonstrate for a selection of both test systems and real power grids. Because our results concern spontaneous synchronization, they are relevant both for reducing dependence on conventional control devices, thus offering an additional layer of protection given that most power outages involve equipment or operational errors, and for contributing to the development of "smart grids" that can recover from failures in real time.

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          Master Stability Functions for Synchronized Coupled Systems

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            Critical phenomena in complex networks

            , , (2007)
            The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, researchers have made important steps toward understanding the qualitatively new critical phenomena in complex networks. We review the results, concepts, and methods of this rapidly developing field. Here we mostly consider two closely related classes of these critical phenomena, namely structural phase transitions in the network architectures and transitions in cooperative models on networks as substrates. We also discuss systems where a network and interacting agents on it influence each other. We overview a wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, k-core percolation, phenomena near epidemic thresholds, condensation transitions, critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks. We also discuss strong finite size effects in these systems and highlight open problems and perspectives.
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              Low dimensional behavior of large systems of globally coupled oscillators.

              It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Lorentzian oscillator frequency distribution function is obtained. Low dimensional behavior is also demonstrated for several prototypical extensions of the Kuramoto model, and time-delayed coupling is also considered. (c) 2008 American Institute of Physics.
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                Author and article information

                Journal
                2013-02-07
                2013-03-01
                Article
                10.1038/NPHYS2535
                1302.1914
                30db6abd-7792-4262-9323-1bcc867f125b

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

                History
                Custom metadata
                A.E. Motter et al, Nature Physics 9, 191-197 (2013)
                Supplementary information available at http://dx.doi.org/10.1038/NPHYS2535
                physics.soc-ph cond-mat.dis-nn nlin.AO

                General physics,Theoretical physics,Nonlinear & Complex systems
                General physics, Theoretical physics, Nonlinear & Complex systems

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