Recovery of Interdependent Networks

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

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arXiv · 1512.02555

Recovery of Interdependent Networks

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

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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 of 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 $\gamma$, 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 $\gamma-p$ 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 avoid the system collapse.

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M. A. Di Muro, C. E. La Rocca, H. E. Stanley, S. Havlin, L. A. Braunstein. 2015-12-08. Recovery of Interdependent Networks. https://arxiv.org/abs/1512.02555

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