Source-linked AI summary
Synchronizing distant nodes: a universal classification of networks
V. Flunkert, S. Yanchuk, T. Dahms, E. Schoell
TL;DR
In delay-coupled networks, synchronization stability depends nontrivially on topology, and the master stability function (MSF) depends on delay. Using large-delay scaling, the paper shows that the MSF becomes rotationally symmetric and increases with coupling magnitude, enabling network classification from spectral properties and synchronized dynamics.
Problem
Synchronization stability in delay-coupled networks depends nontrivially on coupling topology, and the MSF depends on delay times.
Source: p. 1Method
The authors use large-delay scaling to analyze the MSF for fixed points, periodic orbits, and chaotic dynamics.
Source: pp. 1, 3Results
In the large-delay limit, the MSF is rotationally symmetric and either positive and constant or increases with coupling magnitude until a critical radius.
Source: pp. 2–3Takeaways & Limitations
Network synchronizability can be classified from coupling-matrix eigenvalue magnitudes and synchronized dynamics, often without computing the critical radius.
Source: pp. 3–4For large noise strength, the linear theory cannot predict synchronization behavior.
Source: p. 4
Abstract
from arXiv · showhide
Stability of synchronization in delay-coupled networks of identical units generally depends in a complicated way on the coupling topology. We show that for large coupling delays synchronizability relates in a simple way to the spectral properties of the network topology. The master stability function used to determine stability of synchronous solutions has a universal structure in the limit of large delay: it is rotationally symmetric around the origin and increases monotonically with the radius in the complex plane. This allows a universal classification of networks with respect to their synchronization properties and solves the problem of complete synchronization in networks with strongly delayed coupling.