title: 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 analyze 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.
authors: Aix-Marseille Université, Inserm, INS UMR_S 1106, 13005, Marseille, France.|Aix-Marseille Université, CNRS, ISM UMR 7287, 13288, Marseille, France.
authors: Spase
authors: S
authors: Petkoski
authors: Aix-Marseille Université, Inserm, INS UMR_S 1106, 13005, Marseille, France.
authors: Andreas
authors: A
authors: Spiegler
authors: Aix-Marseille Université, Inserm, INS UMR_S 1106, 13005, Marseille, France.
authors: Timothée
authors: T
authors: Proix
authors: Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield S10 2TN, United Kingdom.
authors: Parham
authors: P
authors: Aram
authors: Aix-Marseille Université, CNRS, ISM UMR 7287, 13288, Marseille, France.
authors: Jean-Jacques
authors: JJ
authors: Temprado
authors: Aix-Marseille Université, Inserm, INS UMR_S 1106, 13005, Marseille, France.
authors: Viktor K
authors: VK
authors: Jirsa