噪声环境下时延网络同步的基本限制与折衷
Network Synchronization in a Noisy Environment with Time Delays: Fundamental Limits and Trade-Offs
摘要：
研究了任意网络中线性耦合随机同步问题中非零时滞的影响。利用时滞微分方程理论中已知的精确阈值，给出了任意网络的同步阈值。此外，通过构建潜在波动的标度理论，我们建立了具有均匀时间延迟的噪声环境中同步效率的绝对极限，即，同步景观的宽度的最小可达到值。我们的研究结果也有很强的影响，优化和权衡网络同步延迟。
英文摘要：
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 have also strong implications for optimization and trade-offs in network synchronization with delays.
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