Cascade of failures in coupled network systems with multiple support-dependent relations

Abstract

We study, both analytically and numerically, the cascade of failures in two coupled network systems A and B, where multiple support-dependent relations are randomly built between nodes of networks A and B. In our model we assume that each node in one network can function only if it has at least a single support node in the other network. If both networks A and B are Erdős-Rényi networks, A and B, with (i) sizes $N^A$ and $N^B$, (ii) average degrees $a$ and $b$, and (iii) $c_0^{AB}{N}^B$ support links from network A to B and $c_0^{BA}{N}^B$ support links from network B to A, we find that under random attack with removal of fractions $(1-R^A)N^A$ and $(1-R^B)N^B$ nodes respectively, the percolating giant components of both networks at the end of the cascading failures, ${\mu }_{\infty }^A$ and ${\mu }_{\infty }^B$, are given by the percolation laws ${\mu }_{\infty }^A=R^A[1-\exp (-c_0^{BA}{\mu }_{\infty }^B)][1-\exp (-a{\mu }_{\infty }^A)]$ and ${\mu }_{\infty }^B=R^B[1-\exp (-c_0^{AB}{\mu }_{\infty }^A)][1-\exp (-b{\mu }_{\infty }^B)]$. In the limit of $c_0^{BA}\to \infty$ and $c_0^{AB}\to \infty$, both networks become independent, and the giant components are equivalent to a random attack on a single Erdős-Rényi network. We also test our theory on two coupled scale-free networks, and find good agreement with the simulations.

References in corpus (4)

• Robustness of a Network of Networks
• Robustness of interdependent networks under targeted attack
• How to make a fragile network robust and vice versa
• Percolation on interacting networks

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