具有关联度和频散的噪声振子网络
Networks of noisy oscillators with correlated degree and frequency dispersion
摘要：
我们研究了网络连通性的多样性和节点处的动力学之间的相关性如何影响宏观行为。特别地，我们研究了代表节点动力学的耦合随机相位振子的同步跃迁。在我们的工作中，至关重要的是，节点连接数量的变化与振荡器频率分布的宽度相关。通过对振荡器频率为高斯分布的Erdös-Rényi网络进行数值模拟，我们发现了一个违反直觉的现象，即相关强度的增加伴随着同步开始的临界耦合强度的增加。我们进一步观察到，临界耦合可以只依赖于平均连接数，甚至完全失去其对网络连通性的依赖。只有超过这个状态，加权平均场近似才失效。如果存在噪声，相关性必须更强才能产生类似的观测结果。
英文摘要：
We investigate how correlations between the diversity of the connectivity of networks and the dynamics at their nodes affect the macroscopic behavior. In particular, we study the synchronization transition of coupled stochastic phase oscillators that represent the node dynamics. Crucially in our work, the variability in the number of connections of the nodes is correlated with the width of the frequency distribution of the oscillators. By numerical simulations on Erdös-Rényi networks, where the frequencies of the oscillators are Gaussian distributed, we make the counterintuitive observation that an increase in the strength of the correlation is accompanied by an increase in the critical coupling strength for the onset of synchronization. We further observe that the critical coupling can solely depend on the average number of connections or even completely lose its dependence on the network connectivity. Only beyond this state, a weighted mean-field approximation breaks down. If noise is present, the correlations have to be stronger to yield similar observations.
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。
