# Synchronization in complex oscillator networks and smart grids

@article{Drfler2013SynchronizationIC, title={Synchronization in complex oscillator networks and smart grids}, author={Florian D{\"o}rfler and Michael Chertkov and Francesco Bullo}, journal={Proceedings of the National Academy of Sciences}, year={2013}, volume={110}, pages={2005 - 2010} }

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…

## 734 Citations

### Exploring synchronization in complex oscillator networks

- Computer Science2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
- 2012

A tutorial introduction to coupled oscillator networks, a review of the vast literature on theory and applications, and a collection of different synchronization notions, conditions, and analysis approaches are presented.

### Control of coupled oscillator networks with application to microgrid technologies

- PhysicsScience Advances
- 2015

This work develops a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state.

### Synchronization assessment in power networks and coupled oscillators

- Computer Science, Mathematics2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
- 2012

A novel synchronization condition applicable to a general coupled oscillator model is presented and it is rigorously established that the condition is exact for various interesting network topologies and parameters.

### When is sync globally stable in sparse networks of identical Kuramoto oscillators?

- Mathematics, Computer SciencePhysica A: Statistical Mechanics and its Applications
- 2019

### Optimal synchronization of directed complex networks.

- Computer ScienceChaos
- 2016

Using the generalized synchrony alignment function, it is shown that a network's synchronization properties can be systematically optimized and promoted by a strong alignment of the natural frequencies with the left singular vectors corresponding to the largest singular values of the Laplacian matrix.

### Stability Conditions for Cluster Synchronization in Networks of Heterogeneous Kuramoto Oscillators

- Mathematics, Computer ScienceIEEE Transactions on Control of Network Systems
- 2020

Quantitative conditions on the network weights, cluster configuration, and oscillators’ natural frequency that ensure the asymptotic stability of the cluster synchronization manifold are derived, showing that cluster synchronization is stable when the intracluster coupling is sufficiently stronger than the intercluster coupling.

### Synchronization in complex network system with uncertainty

- Mathematics53rd IEEE Conference on Decision and Control
- 2014

The main contribution of this paper is to provide analytical characterization for the interplay of role played by the internal dynamics of the nonlinear systems, network topology, and uncertainty statistics for the network synchronization.

### Stability Conditions for Cluster Synchronization in Networks of Kuramoto Oscillators

- Mathematics, Computer ScienceArXiv
- 2018

Quantitative conditions on the network weights, cluster configuration, and oscillators' natural frequency that ensure asymptotic stability of the cluster synchronization manifold are derived that ensure the ability to recover the desired cluster synchronization configuration following a perturbation of the oscillators states.

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