Analysis of cascading failure in interdependent networks concerning failure probability and dependent relationship

Interdependent networks have proven to be an important topological structure and exist widely in many real-world systems. Meanwhile, the analysis of cascading failure on interdependent networks is essential for constructing more robust real-world systems. This paper establishes a nonlinear cascade failure model for interdependent networks that incorporate failure probability. First, according to the load redistribution ratios between layers, we present an analytical description of the tolerance threshold for interdependent networks with partial multiple-to-multiple dependency interactions and the failure probability of the overload nodes. Furthermore, simulations of cascading failures triggered by attacks on high-load and low-load nodes are conducted on various networks, respectively. In addition, the study examines how different parameters influence the robustness of interdependent networks. Our results imply that optimizing the inter-layer distribution ratio can significantly enhance network robustness under low-load attacks, while the effect is comparatively weaker under high-load attacks. Additionally, as the failure probability parameter increases, the interdependent network exhibits enhanced robustness. Interestingly, as the interlayer allocation ratio increases, the network’s tolerance threshold initially decreases before rising again. These simulation findings agree well with theoretical results.