Centre for Biomedical Technology, Technical University of Madrid, Pozuelo de Alarcón, Madrid, Spain.
PLoS One. 2011;6(6):e20236. doi: 10.1371/journal.pone.0020236. Epub 2011 Jun 16.
A measure to quantify vulnerability under perturbations (attacks, failures, large fluctuations) in ensembles (networks) of coupled dynamical systems is proposed. Rather than addressing the issue of how the network properties change upon removal of elements of the graph (the strategy followed by most of the existing methods for studying the vulnerability of a network based on its topology), here a dynamical definition of vulnerability is introduced, referring to the robustness of a collective dynamical state to perturbing events occurring over a fixed topology. In particular, we study how the collective (synchronized) dynamics of a network of chaotic units is disrupted under the action of a finite size perturbation on one of its nodes. Illustrative examples are provided for three systems of identical chaotic oscillators coupled according to three distinct well-known network topologies. A quantitative comparison between the obtained vulnerability rankings and the classical connectivity/centrality rankings is made that yields conclusive results. Possible applications of the proposed strategy and conclusions are also discussed.
提出了一种量化耦合动力系统集合（网络）在扰动（攻击、故障、大幅波动）下脆弱性的方法。本文不是针对网络拓扑结构中元素移除时网络属性如何变化的问题（大多数基于拓扑结构研究网络脆弱性的现有方法都是采用这一策略），而是引入了脆弱性的动力学定义，它指的是在固定拓扑结构上发生的扰动事件对集体动力学状态的鲁棒性。具体来说，我们研究了在其节点上发生有限大小的扰动时，网络中混沌单元的集体（同步）动力学是如何被破坏的。针对三个根据三种不同的著名网络拓扑结构耦合的相同混沌振荡器系统，提供了说明性示例。对所得到的脆弱性排名和经典连通性/中心性排名进行了定量比较，得到了明确的结论。还讨论了所提出策略的可能应用和结论。
