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Cascading Failures in Interdependent Networks with Multiple Supply-Demand Links and Functionality Thresholds

M. A. Di Muro, L. D. Valdez, H. H. A. Rêgo, S. V. Buldyrev, H. E. Stanley, L. A. Braunstein

posted on 08 August 2017

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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 were 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 in two interdependent networks, in which each node has its own supply threshold, i.e. a mininum number of supply nodes required to remain functional. In addition, we analyze different conditions of internal failure of a node due to disconnection from nodes belonging to its own network. Here we show that several local conditions of internal failure lead to similar nontrivial results. In the absence of any internal failure condition the model is equivalent to a bipartite system, which can serve as a model of a financial market. We explore rich behaviors of these models resulting in discontinuous and continuous phase transitions. We solve all these models in the thermodynamic limit using the framework of generating functions and stochastic simulations, finding an excellent agreement between them.