Recovery of Interdependent Networks

H. E STANLEY; MATÍAS A. DI MURO; SHLOMO HAVLIN; CRISTIAN E. LA ROCCA; LIDIA A. BRAUNSTEIN

Scientific Reports

Nature Publishing Group

Lugar: Londres; Año: 2016 vol. 6 p. 22834 - 22834

2045-2322

Recent network research has focused on the cascading failures in asystem of interdependent networks and the necessary preconditions forsystem collapse. An important question that has not been addressed ishow to repair a failing system before it suffers total breakdown. Herewe introduce a recovery strategy for nodes and develop an analytic andnumerical framework for studying the concurrent failure and recoveryof a system of interdependent networks based on an efficient andpractically reasonable strategy. Our strategy consists of repairing afraction of failed nodes, with probability of recovery $gamma$, thatare neighbors of the largest connected component of each constituentnetwork. We find that, for a given initial failure of a fraction$1-p$ of nodes, there is a critical probability of recovery abovewhich the cascade is halted and the system fully restores to itsinitial state and below which the system abruptly collapses. As aconsequence we find in the plane $gamma-p$ of the phase diagram threedistinct phases. A phase in which the system never collapses withoutbeing restored, another phase in which the recovery strategy avoidsthe breakdown, and a phase in which even the repairing process cannotprevent system collapse.