Recovery of Interdependent Networks.
Recovery of Interdependent Networks.
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DOI：
10.1038/srep22834
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发表时间：
2016-03-09
影响因子：
4.6
通讯作者：
Braunstein LA
中科院分区：
文献类型：
--
作者：
Di Muro MA;La Rocca CE;Stanley HE;Havlin S;Braunstein LA
最近的网络研究集中在相互依赖的网络系统中的级联故障以及系统崩溃的必要前提条件。一个尚未解决的重要问题是，如何在一个出现故障的系统完全崩溃之前对其进行修复。本文介绍了一种节点恢复策略，并基于一种有效且实用合理的策略，建立了一个分析和数值框架，用于研究相互依赖的网络系统的并发故障和恢复。我们的策略包括修复一部分故障节点，恢复概率为γ，这些节点是每个组成网络的最大连通组件的邻居。我们发现，对于给定的分数为1 − p的节点的初始故障，存在一个临界恢复概率，超过该概率，级联被停止，系统完全恢复到其初始状态，低于该状态，系统突然崩溃。因此，我们在相图的平面γ − p中发现了三个不同的相。一个阶段，其中系统永远不会在不恢复的情况下崩溃，另一个阶段是恢复策略避免崩溃，以及一个即使是修复过程也不能防止系统崩溃的阶段。
Recent network research has focused on the cascading failures in a system of interdependent networks and the necessary preconditions for system collapse. An important question that has not been addressed is how to repair a failing system before it suffers total breakdown. Here we introduce a recovery strategy for nodes and develop an analytic and numerical framework for studying the concurrent failure and recovery of a system of interdependent networks based on an efficient and practically reasonable strategy. Our strategy consists of repairing a fraction of failed nodes, with probability of recovery γ, that are neighbors of the largest connected component of each constituent network. We find that, for a given initial failure of a fraction 1 − p of nodes, there is a critical probability of recovery above which the cascade is halted and the system fully restores to its initial state and below which the system abruptly collapses. As a consequence we find in the plane γ − p of the phase diagram three distinct phases. A phase in which the system never collapses without being restored, another phase in which the recovery strategy avoids the breakdown, and a phase in which even the repairing process cannot prevent system collapse.