The effect of randomness for dependency map on the robustness of interdependent lattices

TL;DR

This paper investigates how the degree of randomness in dependency maps affects the robustness and phase transition behavior of interdependent lattice networks, revealing critical thresholds where the nature of percolation changes.

Contribution

It introduces approximate entropy as a measure of dependency map randomness and analyzes its impact on percolation transitions in interdependent networks.

Findings

Percolation transitions switch from second-order to first-order with increasing randomness.

Critical entropy thresholds determine the nature of the phase transition.

Randomness influences the system's failure dynamics and cascade behavior.

Abstract

For interdependent networks with identity dependency map, percolation is exactly the same with that on a single network and follows a second-order phase transition, while for random dependency, percolation follows a first-order phase transition. In real networks, the dependency relations between networks are neither identical nor completely random. Thus in this paper, we study the influence of randomness for dependency maps on the robustness of interdependent lattice networks. We introduce approximate entropy($ApEn$) as the measure of randomness of the dependency maps. We find that there is critical $ApEn_c$ below which the percolation is continuous, but for larger $ApEn$, it is a first-order transition. With the increment of $ApEn$, the $p_c$ increases until $ApEn$ reaching ${ApEn}_c'$ and then remains almost constant. The time scale of the system shows rich properties as $ApEn$ increases. Our results uncover that randomness is one of the important factors that lead to cascading failures of spatially interdependent networks.