Duan Chao, Nishikawa Takashi, Eroglu Deniz, Motter Adilson E
School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049, China.
Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA.
Sci Adv. 2022 Jul 15;8(28):eabm8310. doi: 10.1126/sciadv.abm8310.
A central issue in the study of large complex network systems, such as power grids, financial networks, and ecological systems, is to understand their response to dynamical perturbations. Recent studies recognize that many real networks show nonnormality and that nonnormality can give rise to reactivity-the capacity of a linearly stable system to amplify its response to perturbations, oftentimes exciting nonlinear instabilities. Here, we identify network structural properties underlying the pervasiveness of nonnormality and reactivity in real directed networks, which we establish using the most extensive dataset of such networks studied in this context to date. The identified properties are imbalances between incoming and outgoing network links and paths at each node. On the basis of this characterization, we develop a theory that quantitatively predicts nonnormality and reactivity and explains the observed pervasiveness. We suggest that these results can be used to design, upgrade, control, and manage networks to avoid or promote network instabilities.
在诸如电网、金融网络和生态系统等大型复杂网络系统的研究中，一个核心问题是了解它们对动态扰动的响应。最近的研究认识到，许多真实网络呈现出非正态性，并且非正态性会引发反应性——一个线性稳定系统放大其对扰动响应的能力，常常激发非线性不稳定性。在这里，我们确定了真实有向网络中非正态性和反应性普遍存在背后的网络结构特性，我们使用了迄今为止在这方面研究的此类网络最广泛的数据集来建立这些特性。所确定的特性是每个节点处入向和出向网络链路及路径之间的不平衡。基于这一特征，我们发展了一种理论，该理论定量预测非正态性和反应性，并解释所观察到的普遍性。我们认为，这些结果可用于设计、升级、控制和管理网络，以避免或促进网络不稳定性。
