Noise stability of synchronization and optimal network structures
arXiv:2001.06768 · doi:10.1063/1.5121341
Abstract
We provide a theoretical framework for quantifying the expected level of synchronization in a network of noisy oscillators. Through linearization around the synchronized state, we derive 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: the magnitude of the fluctuations around a synchronized state and the disturbance coefficients that represent how strongly node disturbs the synchronization. With this approach, we can quantify the effect of individual nodes and links on synchronization. Our theory can thus be utilized to find the optimal network structure for accomplishing the best synchronization. Furthermore, when the noise levels of the oscillators are heterogeneous, we can also find optimal oscillator configurations, i.e., where to place oscillators in a given network depending on their noise levels. We apply our theory to several example networks to elucidate optimal network structures and oscillator configurations.
arXiv commentTo appear in Chaos
References in corpus (16)
- Synchronization in complex networks
- Synchronization in small-world systems
- Turing patterns in network-organized activator-inhibitor systems
- Turing patterns on networks
- Coupling functions: Universal insights into dynamical interaction mechanisms
- Synchronization is optimal in non-diagonalizable networks
- Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations
- Collective dynamical response of coupled oscillators with any network structure
- Improving the Frequency Precision of Oscillators by Synchronization
- Structure of Cell Networks Critically Determines Oscillation Regularity
- Clustering in Globally Coupled Oscillators Near a Hopf Bifurcation: Theory and Experiments
- Impact of hierarchical modular structure on ranking of individual nodes in directed networks
- Analysis of relative influence of nodes in directed networks
- Global Robustness vs. Local Vulnerabilities in Complex Synchronous Networks
- Collective frequency variation in network synchronization and reverse PageRank
- Thermodynamic Characterization of Synchronization-Optimized Oscillator-Networks