Network coordination and synchronization in a noisy environment with time delays

2012/09/30 by D. Hunt, David Hunt, Bolesław K. Szymański +2
Computer Science · Physics and Astronomy · #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #Opinion Dynamics and Social Influence #cond-mat.dis-nn #cond-mat.stat-mech #cs.MA #nlin.CD

paper · pdf · doi:10.1103/physreve.86.056114

published as Phys. Rev. E 86, 056114 (2012) · final version, reflecting changes in response to referees' comments

arxiv created 2012/11/30 · openalex publication_date 2012/11/30 · arxiv updated 2012/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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