Source-linked AI summary
Optimal synchronization of complex networks
Per Sebastian Skardal, Dane Taylor, Jie Sun
TL;DR
The relation between network structure and heterogeneous oscillator frequencies remains unclear, complicating synchronization optimization. The paper derives an optimizable synchrony alignment function and finds that dominant-eigenvector alignment and matching network and frequency heterogeneity promote synchrony.
Problem
How can synchronization be optimized when it depends jointly on oscillator frequencies and network structure, a relationship that remains incompletely understood?
Source: p. 1Method
The authors derive a synchrony alignment function from the oscillator dynamics and use its minimization to guide frequency allocation or network design.
Source: pp. 1–2Results
Synchronization is promoted by aligning frequencies with dominant Laplacian eigenvectors and matching network heterogeneity to frequency heterogeneity.
Source: pp. 3–4Takeaways & Limitations
In optimized networks, large frequencies localize to hubs and neighboring oscillators’ frequencies are negatively correlated.
Source: p. 4The analysis assumes strong coupling (r≈1), and extension beyond the phase-oscillator model to Landau–Stuart, Winfree, or chaotic oscillators remains open.
Source: pp. 1, 4
Abstract
from arXiv · showhide
We study optimal synchronization in networks of heterogeneous phase oscillators. Our main result is the derivation of a synchrony alignment function that encodes the interplay between network structure and oscillators' frequencies and can be readily optimized. We highlight its utility in two general problems: constrained frequency allocation and network design. In general, we find that synchronization is promoted by strong alignments between frequencies and the dominant Laplacian eigenvectors, as well as a matching between the heterogeneity of frequencies and network structure.