Hunt D, Szymanski B K, Korniss G
Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056114. doi: 10.1103/PhysRevE.86.056114. Epub 2012 Nov 30.
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.
我们研究了复杂网络中具有线性耦合的随机同步问题中，非零时间延迟的影响。我们考虑两种类型的时间延迟：相互作用节点之间的传输延迟和每个节点处的局部延迟（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，我们获得了同步阈值（相位边界）以及同步景观宽度的标度行为，在某些情况下适用于任意网络，而在其他情况下适用于特定加权网络。当无法获得直接解析结果时，数值计算可用于探索这些网络的行为。我们评论了这些发现对于简单的局部或全局加权网络耦合的意义，以及此类系统中可能存在的权衡。
