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.

References in corpus (5)

• Synchronization in complex networks
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Macroscopic description for networks of spiking neurons
• Shear diversity prevents collective synchronization
• Routes to synchrony between asymmetrically interacting oscillator ensembles

Cited by in corpus (5)

• Chimera states in uncoupled neurons induced by a multilayer structure
• Analytical prediction of specific spatiotemporal patterns in nonlinear oscillator networks with distance-dependent time delays
• Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling
• Emerging chimera states under non-identical counter-rotating oscillators
• Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions