时滞随机网络协调中的极值波动
Extreme Fluctuations in Stochastic Network Coordination with Time Delays
摘要：
研究了均匀时滞对复杂网络中线性耦合随机同步与协调问题中极端涨落的影响。我们从网络的基本模式的行为中获得节点处波动的平均大小。然后，我们得到的极端波动的标度行为与系统的大小，以及在复杂的网络上的极端的分布，并比较它们与规则的一维格子。对于大型复杂网络，当延迟不太接近临界延迟时，节点处的波动有效地解耦，极限分布收敛到Fisher-Tippett-Gumbel密度。相比之下，低维空间图中的波动是强烈相关的，并且极端的极限分布是艾里密度。最后，我们还探讨了非线性耦合的稳定性和极端的同步景观的影响。
英文摘要：
We study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks. We obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network. We then obtain the scaling behavior of the extreme fluctuations with system size, as well as the distribution of the extremes on complex networks, and compare them to those on regular one-dimensional lattices. For large complex networks, when the delay is not too close to the critical one, fluctuations at the nodes effectively decouple, and the limit distributions converge to the Fisher-Tippett-Gumbel density. In contrast, fluctuations in low-dimensional spatial graphs are strongly correlated, and the limit distribution of the extremes is the Airy density. Finally, we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes.
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