噪声网络中的集体涨落
Collective fluctuations in networks of noisy components
摘要：
集体动力学是由嘈杂的动力学成分之间的相互作用产生的。例子包括心跳、昼夜节律和各种斑图形成。由于每个组件中的噪声，集体动力学不可避免地涉及波动，这可能会对系统的功能产生关键影响。然而，孤立的个体成分的波动与集体动力学的波动之间的关系尚不清楚。在这里，我们研究了一个线性动力系统的网络组件进行独立的高斯噪声和分析表明，网络的连通性决定了集体动力学的波动强度。值得注意的是，在包括无标度网络在内的一般有向网络中，波动随系统规模的减小比中心极限定理所述的标准定律慢得多。当网络存在全局方向性时，它们甚至在大系统规模下仍然是有限的。此外，这种非平凡的行为，甚至出现在无向网络时，考虑非线性动力系统。我们用一个耦合振荡器系统证明了这一点。
英文摘要：
Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve fluctuations, which may crucially affect functioning of the system. However, the relation between the fluctuations in isolated individual components and those in collective dynamics is unclear. Here we study a linear dynamical system of networked components subjected to independent Gaussian noise and analytically show that the connectivity of networks determines the intensity of fluctuations in the collective dynamics. Remarkably, in general directed networks including scale-free networks, the fluctuations decrease more slowly with the system size than the standard law stated by the central limit theorem. They even remain finite for a large system size when global directionality of the network exists. Moreover, such nontrivial behavior appears even in undirected networks when nonlinear dynamical systems are considered. We demonstrate it with a coupled oscillator system.
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。
