小世界是最快的吗？
Do Small Worlds Synchronize Fastest?
摘要：
小世界网络介于完全规则和完全随机拓扑之间，同时表现出大的局部聚类和短的平均路径长度。因此，小世界拓扑被建议用于支持网络同步。本文研究了广义Watts-Strogatz系综中耦合振子同步的渐近速度与其相互作用拓扑的随机性程度的关系。我们发现，具有固定入度的网络同步速度越快，它们的随机性越大，而小世界只是作为一种中间情况出现。对于任何通用网络系综，如果同步速度在中等随机性下处于极端状态，那么它在小世界区域中是最慢的。这种现象发生在各种类型的振荡器，内禀动力学和耦合方案。
英文摘要：
Small world networks interpolate between fully regular and fully random topologies and simultaneously exhibit large local clustering as well as short average path length. Small world topology has therefore been suggested to support network synchronization. Here we study the asymptotic speed of synchronization of coupled oscillators in dependence on the degree of randomness of their interaction topology in generalized Watts-Strogatz ensembles. We find that networks with fixed in-degree synchronize faster the more random they are, with small worlds just appearing as an intermediate case. For any generic network ensemble, if synchronization speed is at all extremal at intermediate randomness, it is slowest in the small world regime. This phenomenon occurs for various types of oscillators, intrinsic dynamics and coupling schemes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
