带时延噪声环境下的网络协调与同步
Network Coordination and Synchronization in a Noisy Environment with Time Delays
摘要：
研究了复杂网络中线性耦合随机同步问题中非零时滞的影响。我们考虑两种类型的时间延迟：交互节点之间的传输延迟和每个节点的本地延迟（由于处理，认知或执行延迟）。通过研究几种延迟方案的潜在波动，我们获得了同步性阈值（相位边界）和同步景观宽度的缩放行为，在某些情况下，对于任意网络和其他特定加权网络。数值计算允许这些网络的行为进行探索时，直接的分析结果是不可用的。我们评论这些发现的影响，简单的本地或全球加权网络耦合和可能的权衡存在于这样的系统。
英文摘要：
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.
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