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Di Muro MA, La Rocca CE, Stanley HE, et al. Recovery of Interdependent Networks. Sci Rep. 2016;6:22834doi: 10.1038/srep22834.
Di Muro, M. A., La Rocca, C. E., Stanley, H. E., Havlin, S., & Braunstein, L. A. (2016). Recovery of Interdependent Networks. Scientific reports, 622834. https://doi.org/10.1038/srep22834
Di Muro, M A, et al. "Recovery of Interdependent Networks." Scientific reports vol. 6 (2016): 22834. doi: https://doi.org/10.1038/srep22834
Di Muro MA, La Rocca CE, Stanley HE, Havlin S, Braunstein LA. Recovery of Interdependent Networks. Sci Rep. 2016 Mar 09;6:22834. doi: 10.1038/srep22834. PMID: 26956773; PMCID: PMC4783785.
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Sci Rep. 2016 Mar 09;6:22834. doi: 10.1038/srep22834.

Recovery of Interdependent Networks.

Scientific reports

M A Di Muro, C E La Rocca, H E Stanley, S Havlin, L A Braunstein

Affiliations

  1. Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR)-Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata-CONICET, Funes 3350 (7600) Mar del Plata, Argentina.
  2. Center for Polymer Studies, Boston University, Boston, Massachusetts 02215, USA.
  3. Department of Physics, Bar Ilan University, Ramat Gan, Israel.

PMID: 26956773 PMCID: PMC4783785 DOI: 10.1038/srep22834

Abstract

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.

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