Percolation Of The Interdependent Networks

In the recently network age, a variety of networks provide great support to the improvement of people’s living quality, social progress and the development of economy, but also bring us many problems, such as unplugging, traffic congestion and the transmission of network virus. These problems ultimately attributed to network security,thus studing the structure characteristics and stability of network has important practical significance. Early studies of complex networks are mainly focus on a single network. But with the development of society and the progress of network technology, dependence relation are more general between networks, becoming as interdependent networks. In the interdependent networks, some failure nodes will lead to its dependent node also being failure, cascading failure through the network. The cascading failure often leads to the collapse of the system. Early researching of interdependent network, researcher usually study the interdependent networks or infrastructure system by means of engineering science, statistics and other ways. Until 2010, S.V.Buldyrev et al. developed a mathematical framework by using percolation theory and the generating function for understanding interdependent network, so that the research of interdependent netwoks go towards a new stage.Study of interdependent network mainly involves the cascade control and defense, attack strategy, cascade model and the robustness of the network. In this article, with percolation theory and the generating function means, we study a cascade interdependent network failure mechanism and targeted-attack model respectively. Firstly, we study how the cascading failure impact on the network percolation phase.we proposes an avoiding cascading failure model.We find that there is a parameter regionmin max[, ]c cq q, when the control parameters cminq ?q, the percolation phase transition goes second order, and when the q is in min max[, ]c cq q, it is a hybrid phase, which a first order and the second order exist. When cmaxq ?q, the percolation phase transition is a classical first order.This results show that the reduction of q can effectively slow down the cascading failure. Secondly, we study the percolation phase transition on targeted-attack model,and proposes a targeted-attack model denpending on vertex’s degree and its dependent vertex’s degree. We find that damage to the network reduce when high degree nodes have low probability to failure, but the probability is reduced to a certain value, it will not reduce any more. In addition,in the scale-free network, we also found that only high degree nodes in both networks being protected with a low probability to be attacked can improve the robustness of the interdependent network.This results show that vertex’s degree and its dependent vertex’s degree have different effects in different networks structure under different attacks.