Research On The Cascade And Cascade Control On Coupled Networks

Cascading failure has become one of research hotspots in complex network, which attracts a lot of attention from scholars at home and abroad. It focuses on the partial failure causing catastrophic damage to the whole system. The relative discussion is helpful to understand the inner mechanism of wholesale collapse, and to improve the safety and reliability of modern infrastructures etc. In recent years, with the rapid development of science and technology, all kinds of infrastructure systems are more closely interdependent to each other. The proposed cou-pled networks model deepens people’s understanding on the internal mechanism of modern complex systems. So, study of cascading failure of coupled network has great practical significance. Considering the diversity of dependency, there are two typical coupled network models:the interconnected network and the interdependent network. This paper discusses the above models and provides relative protection strategy. It is hoped that our research can provide feasible suggestions for the real systems design and protection.Firstly, in most of the corresponding results, the topologies of the networks are destroyed during cascading failure. Here, we present an interconnected network model considering cascading failures based on the dynamic redistribution of flow in the networks. Compared with the results of single scale-free networks, we find that interconnected scale-free networks have higher vulnerability. Additionally, the network heterogeneity plays an important role in the robustness of interconnected networks under intentional attacks. Considering the effects of various coupling preferences, the results show that there are almost no differences Finally, the application of our model to the Beijing interconnected traffic network, which consists of a subway network and a bus network, shows that the subway network suffers more damage under the attack. Moreover, the interconnected traffic network may be more exposed to damage after initial attacks on the bus network. These discussions are important for the design and optimization of interconnected networks.Secondly, our previous work has focused on the robustness of interdependent networks with loads, finding that interdependent scale-free networks show extreme vulnerability. Moreover, there exists a "valley" of scaling exponent for which the interdependent network exhibits minimal robustness. Because of the strong vulnerability of interdependent network, the study of cascade control is very meaningful. In this paper, the costless protection strategy in single networks is applied to interdependent networks, but this will make the interdependent networks suffer more damage in most cases. Then, in view of the dependence of two layers in interdependent networks, we present an extended costless protection strategy which drastically reduces the size of the cascading. In some cases, after the extended strategy is applied, the robustness will be more than three times higher than that without protection. Additionally, we find that the network heterogeneity plays an important role in the effect of our defense strategy. By adjusting the intensity of defense strategy, we show that the interdependent networks can reach an optimal robustness against the intentional attacks.This work presents a model for cascading failures based on the dynamical redistribution of the flow on the interconnected network, and provides a kind of costless protection strategy on the interdependent network. This will contribute to reveal the evolution rules and the features of cascading failure on the infrastructure networks such as the transportation network, power grid, transport network and Internet. Moreover, these theories have profound guiding significance for protecti-ng the safe running of the infrastructure networks. Meanwhile, in the situation of complex, changeable and coupled external environment, this work also provides new theory and method for the network security induced by abnormal behaviors and suggestion with realistic significance.