Zhang Xiaozhu, Ma Cheng, Timme Marc
Chair for Network Dynamics, Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), Cluster of Excellence Physics of Life, Technical University of Dresden, 01062 Dresden, Germany.
School of Physics, Nankai University, Tianjin 300071, China.
Chaos. 2020 Jun;30(6):063111. doi: 10.1063/1.5122963.
Vulnerability of networks has so far been quantified mainly for structural properties. In driven systems, however, vulnerability intrinsically relies on the collective response dynamics. As shown recently, dynamic response patterns emerging in driven oscillator networks and AC power grid models are highly heterogeneous and nontrivial, depending jointly on the driving frequency, the interaction topology of the network, and the node or nodes driven. Identifying which nodes are most susceptible to dynamic driving and may thus make the system as a whole vulnerable to external input signals, however, remains a challenge. Here, we propose an easy-to-compute Dynamic Vulnerability Index (DVI) for identifying those nodes that exhibit largest amplitude responses to dynamic driving signals with given power spectra and thus are most vulnerable. The DVI is based on linear response theory, as such generic, and enables robust predictions. It thus shows potential for a wide range of applications across dynamically driven networks, for instance, for identifying the vulnerable nodes in power grids driven by fluctuating inputs from renewable energy sources and fluctuating power output to consumers.
到目前为止，网络的脆弱性主要是根据结构特性来量化的。然而，在受驱动系统中，脆弱性本质上依赖于集体响应动力学。最近的研究表明，在受驱动的振荡器网络和交流电网模型中出现的动态响应模式高度异质且复杂，这共同取决于驱动频率、网络的相互作用拓扑结构以及被驱动的一个或多个节点。然而，确定哪些节点最容易受到动态驱动影响，进而可能使整个系统容易受到外部输入信号的影响，仍然是一个挑战。在此，我们提出一种易于计算的动态脆弱性指数（DVI），用于识别那些对具有给定功率谱的动态驱动信号表现出最大幅度响应、因而最脆弱的节点。该DVI基于线性响应理论，具有通用性，能够做出可靠的预测。因此，它在广泛的动态驱动网络中显示出应用潜力，例如，用于识别由可再生能源的波动输入和向消费者的波动功率输出所驱动的电网中的脆弱节点。
