Abstract
We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in an arbitrary network. Using the known exact threshold value from the theory of differential equations with delays, we provide the synchronizability threshold for an arbitrary network. Further, by constructing the scaling theory of the underlying fluctuations, we establish the absolute limit of synchronization efficiency in a noisy environment with uniform time delays, i.e., the minimum attainable value of the width of the synchronization landscape. Our results also have strong implications for optimization and trade-offs in network synchronization with delays.
- Received 19 May 2010
DOI:https://doi.org/10.1103/PhysRevLett.105.068701
© 2010 The American Physical Society
Synopsis
Don’t micromanage when communication is delayed
Published 20 August 2010
Reducing coordination among local nodes in a network suffering from time lags can improve the overall performance of the entire network.
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