Cascading failures in interdependent lattice networks: The critical role of the length of dependency links

Wei Li, Amir Bashan, Sergey V. Buldyrev, H. Eugene Stanley, Shlomo Havlin

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225 Scopus citations

Abstract

We study the cascading failures in a system composed of two interdependent square lattice networks A and B placed on the same Cartesian plane, where each node in network A depends on a node in network B randomly chosen within a certain distance r from the corresponding node in network A and vice versa. Our results suggest that percolation for small r below r max8 (lattice units) is a second-order transition, and for larger r is a first-order transition. For r<r max, the critical threshold increases linearly with r from 0.593 at r=0 and reaches a maximum, 0.738 for r=r max, and then gradually decreases to 0.683 for r=. Our analytical considerations are in good agreement with simulations. Our study suggests that interdependent infrastructures embedded in Euclidean space become most vulnerable when the distance between interdependent nodes is in the intermediate range, which is much smaller than the size of the system.

Original languageEnglish
Article number228702
JournalPhysical Review Letters
Volume108
Issue number22
DOIs
StatePublished - 1 Jun 2012

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