Heterogeneity of time delays determines synchronization of coupled oscillators
Abstract
Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyse delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.
Cite
@article{arxiv.1606.08613,
title = {Heterogeneity of time delays determines synchronization of coupled oscillators},
author = {Spase Petkoski and Andreas Spiegler and Timothée Proix and Parham Aram and Jean-Jacques Temprado and Viktor K. Jirsa},
journal= {arXiv preprint arXiv:1606.08613},
year = {2016}
}