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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.
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https://hal.archives-ouvertes.fr/hal-01431271
Contributor : Viktor Jirsa <>
Submitted on : Tuesday, January 10, 2017 - 4:32:35 PM
Last modification on : Tuesday, April 21, 2020 - 10:29:59 AM

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Spase Petkoski, Andreas Spiegler, Timothée Proix, Parham Aram, Jean-Jacques Temprado, et al.. Heterogeneity of time delays determines synchronization of coupled oscillators. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2016, 94 (1), ⟨10.1103/PhysRevE.94.012209⟩. ⟨hal-01431271⟩

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