Cascading Failures in Interdependent Networks with Multiple Supply-Demand Links and Functionality Thresholds.
Cascading Failures in Interdependent Networks with Multiple Supply-Demand Links and Functionality Thresholds.
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DOI：
10.1038/s41598-017-14384-y
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发表时间：
2017-11-08
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;Valdez LD;Aragão Rêgo HH;Buldyrev SV;Stanley HE;Braunstein LA
各种社会、金融、生物和技术系统可以通过相互依赖的网络来建模。已经假设，为了保持功能，一个网络中的节点必须接受来自属于不同网络的节点的支持。到目前为止，这些模型仅限于这样的情况：只有当节点失去所有供应节点时，故障才会在网络中传播。本文对两个相互依赖的网络建立了一个更现实的模型，其中每个节点都有自己的供应阈值，即它们需要最少数量的供应节点的支持才能维持运行。此外，我们还分析了内部节点因与自身网络内的节点断开连接而发生故障的不同情况。我们证明了几个局部内部失效条件会导致类似的非平凡结果。当不存在内部故障时，该模型等价于一个二部系统，这对于对金融市场进行建模是有用的。我们探索了这些模型的丰富行为，包括间断相变和连续相变。利用母函数形式，我们在无限大网络的极限下对所有模型进行了解析求解，得到了与随机模拟很好的一致性。
Various social, financial, biological and technological systems can be modeled by interdependent networks. It has been assumed that in order to remain functional, nodes in one network must receive the support from nodes belonging to different networks. So far these models have been limited to the case in which the failure propagates across networks only if the nodes lose all their supply nodes. In this paper we develop a more realistic model for two interdependent networks in which each node has its own supply threshold, i.e., they need the support of a minimum number of supply nodes to remain functional. In addition, we analyze different conditions of internal node failure due to disconnection from nodes within its own network. We show that several local internal failure conditions lead to similar nontrivial results. When there are no internal failures the model is equivalent to a bipartite system, which can be useful to model a financial market. We explore the rich behaviors of these models that include discontinuous and continuous phase transitions. Using the generating functions formalism, we analytically solve all the models in the limit of infinitely large networks and find an excellent agreement with the stochastic simulations.
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