Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.
Phys Rev Lett. 2010 Aug 6;105(6):068701. doi: 10.1103/PhysRevLett.105.068701. Epub 2010 Aug 4.
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.
我们研究了具有任意网络中线性耦合的随机同步问题中非零时间延迟的影响。使用具有延迟的微分方程理论中的已知精确阈值，我们为任意网络提供了可同步性阈值。此外，通过构建基础波动的标度理论，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，即同步景观的最小可达到宽度。我们的结果对具有延迟的网络同步中的优化和权衡也具有重要意义。
