Network Coordination and Synchronization in a Noisy Environment with Time Delays

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.

final version, reflecting changes in response to referees' comments

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Cited by in corpus (9)

• Synchronization of networks of oscillators with distributed delay coupling
• Extreme Fluctuations in Stochastic Network Coordination with Time Delays
• Analytic relationship of relative synchronizability to network structure and motifs
• Influence of time delay on information exchanges between coupled linear stochastic systems
• The effect of distributed time-delays on the synchronization of neuronal networks
• Biharmonic Distance and the Performance of Second-Order Consensus Networks with Stochastic Disturbances
• Risk of Collision and Detachment in Vehicle Platooning: Time-Delay-Induced Limitations and Trade-Offs (Extended Version)
• Fluctuations of a surface relaxation model in interacting scale free networks
• Performance Improvement in Noisy Linear Consensus Networks with Time-Delay