Network Coordination and Synchronization in a Noisy Environment with Time Delays

TL;DR

This paper investigates how nonzero time delays affect stochastic synchronization in complex networks, analyzing thresholds and scaling behaviors through analytical and numerical methods.

Contribution

It introduces a comprehensive analysis of transmission and local delays in network synchronization, providing new insights into stability thresholds and fluctuation scaling.

Findings

Identified synchronization thresholds for various delay schemes.

Derived scaling laws for the width of the synchronization landscape.

Numerical results complement analytical findings for complex networks.

Abstract

We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in complex networks. We consider two types of time delays: transmission delays between interacting nodes and local delays at each node (due to processing, cognitive, or execution delays). By investigating the underlying fluctuations for several delay schemes, we obtain the synchronizability threshold (phase boundary) and the scaling behavior of the width of the synchronization landscape, in some cases for arbitrary networks and in others for specific weighted networks. Numerical computations allow the behavior of these networks to be explored when direct analytical results are not available. We comment on the implications of these findings for simple locally or globally weighted network couplings and possible trade-offs present in such systems.