Large coupled oscillator systems with heterogeneous interaction delays

TL;DR

This paper investigates how heterogeneous communication delays influence the dynamics of large coupled oscillator systems, revealing that delay distribution significantly affects stability and transition behaviors.

Contribution

It introduces a modified Kuramoto model with delay distribution and derives reduced equations to analyze stability and dynamical transitions.

Findings

Delay spread can destabilize incoherent states.

Heterogeneous delays alter transition thresholds.

Delay distribution impacts system synchronization.

Abstract

In order to discover generic effects of heterogeneous communication delays on the dynamics of large systems of coupled oscillators, this paper studies a modification of the Kuramoto model incorporating a distribution of interaction delays. By focusing attention on the reduced dynamics on an invariant manifold of the original system, we derive governing equations for the system which we use to study stability of the incoherent states and the dynamical transitional behavior from stable incoherent states to stable coherent states. We find that spread in the distribution function of delays can greatly alter the system dynamics.