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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
TL;DR
The paper examines how spatial constraints and dependency-link lengths affect cascading failures in interdependent lattice networks. It models mutual percolation between two spatially embedded lattices and finds that transition order and critical thresholds depend strongly on dependency distance.
Problem
Most prior robustness studies focused on random interdependent networks, motivating analysis of spatially embedded networks with dependency links restricted to distance r.
Method
The study analyzes mutual percolation in two interdependent square lattices, where each node depends on a node in the other lattice within distance r.
Results
For r below rmax ≈ 8, the transition is second-order; for larger r, it becomes first-order, with the critical threshold reaching 0.738 at r = rmax and decreasing to 0.683 at r = ∞.
Takeaways & Limitations
The square-lattice model can serve as a benchmark for more complex spatially embedded networks, whose two-dimensional percolation behavior has universal scaling under finite characteristic link lengths.
Takeaways & Limitations
The reported interface-threshold results use an artificial model in which a flat interface is initially created, although random removal may create such an interface through fluctuations.
Abstract
from arXiv · showhide
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 $r_{\rm max}\approx 8$ (lattice units) is a second-order transition, and for larger $r$ is a first-order transition. For $r<r_{\rm max}$, the critical threshold increases linearly with $r$ from 0.593 at $r=0$ and reaches a maximum, 0.738 for $r=r_{\rm max}$ and then gradually decreases to 0.683 for $r=\infty$. 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.