Research On The Cascading Failures In Interdependent Networks

As the development of science and technology, various infrastructure systems are increasingly dependent on each other. The previous researches of the single networks can hardly represent the robustness of network system in which such dependence exists. Hence, only can the analysis of interdependent networks’robustness accurately help to realize the crucial factors of real world system safety and stability.In this paper, the interdependence of networks in reality and load of the nodes are combined so as to model the interdependent networks in a more realistic methodology. Meanwhile, based on the often used cascading failure model, we choose the load-capacity as the theoretical guidance of the cascading failure within interdependent networks with load.To search the factors and the key nodes with certain influence on the robustness of interdependent network, we study the robustness under different attack strategies respect to structurally different interdependent network. Further, by applying the percolation theory and intentional attack to trigger the cascading failure process on the interdependent networks, the robustness of different networks is characterized. Generally in the study of percolation, while certain proportion nodes are removed within the interdependent network, when considering load, first-order phase transition are featured in our research with respect to structurally different networks as well as their phase transition types with contrast to the second-order phase transition in previous publications. It suggests the abruptness of the emergence of large-scale collapse. When compared to the networks without any consideration of load, the transition threshold value increases considerably. Hence system-wise collapse is expected when only a small proportion of nodes are removed. These facts imply that in the case of removal of single node, more damages to networks are caused by intentional attack than random removal and that the weaker robustness of network system with interdependence against intentional attack is expected. They in turn suggest that to improve the robustness of interdependent network against attack, the tolerance of network nodes should be increased.It is therefore suggested that the interdependent networks with loads are much vulnerable than single networks or interdependent networks without loads. Thus, it is critical to search for the protection strategy to stabilize the system under attack. We conclude that the previously-used single network protection strategy, when apply to the model in our research, displays desirable effect when the heterogeneous networks and small tolerance are considered. More generally, this so-called protection can not only act positively but also cause further damage. Viewing this, we propose improved protection tactics lying on the mutual interdependent relationships, which reveals considerably better effect when applying to heterogeneous networks-more than half of functionality of nearly broke-down network are preserved.This study on robustness and protection shows that the interdependence tend to render the network vulnerable, while turning the previously effective protection strategy to a devastating one. Hence, it might be essential to study and comprehend the interdependence for the infrastructure secure and stability. It is hoped that our research can provide valuable reference to subsequent study on robustness of interdependent networks as well as protection strategy, and some effective and feasible alternatives for the real-world network construction and protection.