# Collective frequency variation in network synchronization and reverse PageRank.

@article{Skardal2016CollectiveFV, title={Collective frequency variation in network synchronization and reverse PageRank.}, author={Per Sebastian Skardal and Dane Taylor and Jie Sun and Alex Arenas}, journal={Physical review. E}, year={2016}, volume={93}, pages={ 042314 } }

A wide range of natural and engineered phenomena rely on large networks of interacting units to reach a dynamical consensus state where the system collectively operates. Here we study the dynamics of self-organizing systems and show that for generic directed networks the collective frequency of the ensemble is not the same as the mean of the individuals' natural frequencies. Specifically, we show that the collective frequency equals a weighted average of the natural frequencies, where the…

## 12 Citations

### 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.

### Geometric unfolding of synchronization dynamics on networks.

- MathematicsChaos
- 2021

We study the synchronized state in a population of network-coupled, heterogeneous oscillators. In particular, we show that the steady-state solution of the linearized dynamics may be written as a…

### Diffusion dynamics and synchronizability of hierarchical products of networks.

- PhysicsPhysical review. E
- 2017

This work applies techniques previously used for approximating the eigenvalues of the adjacency matrix to the Laplacian matrix, allowing it to quantify the effects that the primary and secondary subnetworks have on diffusion and synchronization in terms of a coupling parameter that weighs the secondary subnetwork relative to the primary subnetwork.

### Network Synchronization with Uncertain Dynamics

- Computer Science
- 2019

This work extends the Synchrony Alignment Function (SAF) framework to analyze network-coupled oscillators with heterogeneous natural frequencies that are drawn as a multivariate random vector and obtains expressions for the expectation and variance of the SAF for given network structures.

### Synchronization of Network-Coupled Oscillators with Uncertain Dynamics

- Computer ScienceSIAM J. Appl. Math.
- 2019

This work extends the Synchrony Alignment Function (SAF) framework to analyze network-coupled oscillators with heterogeneous natural frequencies that are drawn as a multivariate random vector and obtains expressions for the expectation and variance of the SAF for given network structures.

### Functional control of oscillator networks

- Computer ScienceNature Communications
- 2022

This work presents a principled method to prescribe exact and robust functional configurations from local network interactions through optimal tuning of the oscillators’ parameters, and derives algebraic and graph-theoretic conditions to guarantee the feasibility and stability of target functional patterns.

### Noise stability of synchronization and optimal network structures.

- Computer ScienceChaos
- 2020

This work provides a theoretical framework for quantifying the expected level of synchronization in a network of noisy oscillators and derives the following quantities as functions of the eigenvalues and eigenfunctions of the network Laplacian using a standard technique for dealing with multivariate Ornstein-Uhlenbeck processes.

### Optimal phase synchronization in networks of phase-coherent chaotic oscillators.

- PhysicsChaos
- 2017

It is shown by means of numerical and experimental results that it is possible to define a synchrony alignment function J(ω,L) linking the natural frequencies of a set of non-identical phase-coherent chaotic oscillators with the topology of the Laplacian matrix L, the latter accounting for the specific organization of the network of interactions between oscillators.

### Synchronization of Heterogeneous Oscillators Under Network Modifications: Perturbation and Optimization of the Synchrony Alignment Function

- Physics, Computer ScienceSIAM J. Appl. Math.
- 2016

This work studies how network modifications affect the synchronization properties of network-coupled dynamical systems that have heterogeneous node dynamics (e.g., phase oscillators with non-identical frequencies), which is often the case for real-world systems.

### Controlling the collective behaviour of networks of heterogenous Kuramoto oscillators with phase lags

- Mathematics2018 European Control Conference (ECC)
- 2018

Analytical conditions are found that allow to determine the control effort required to guarantee convergence of all the oscillators towards a common collective evolution despite the presence of heterogeneities and phase lags.

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