Cascades On Interconnected Networks

With the rapid development of the information technology, human society has en-tered an era of complex networks. Over the last decade, as a new interdisciplinary field, complex networks have undergone rapid development. In the field of complex networks, on one hand, the researches on the network topology help us understand complex systems; on the other hand, the network dynamics studies help people portray the essence of complex systems. Under this condition, the studies on complex networks have received more and more attention. In particularly, cascading failures on complex networks have been a hot topic recently. In communication networks, for example, a s-mall number of routers are overloaded and fail, then the information flow on the failed routers will be transmitted through other routers, which could lead to other routers overloaded and fail. Eventually it will make massive routers out of work, and the en-tire network collapses. Once this massive failure occurs, it will cause great damage. In the studies of cascading failures on complex networks, scholars have established cor-responding models to study the complex network robustness against cascading failures and proposed protective methods to improve the networks robustness. Considering that the real-world networks often interact and influence with each other, more and more researchers are interested in the study on coupled networks. In this thesis, we explored cascading failures in interconnected networks which is composed of more than one network, coupled by interconnected links between them. By analyzing various fac-tors affecting this dynamic in interconnection networks (such as coupling possibility, coupling preference, network capacity, and network size, etc.), we can have deeper understanding of the combined effects of various factors on interconnected network-s. And these findings may provide guidance for the design and optimization of real interconnection networks. In this paper, the main contents and results are as follows:(1) We analyze the effect of network capacity on the robustness of interconnected net-works. We find that when the capacity of one network is fixed, the robustness of the whole system does not necessarily follow another network's capacity. More specifically, when the capacity of the fixed network is very large or very smal-1, the robustness of the whole system increases as another network's capacity increases. But when the fixed network capacity is neither very small nor very large, as another network capacity increases, the robustness of the whole system decreases first and then increases. Moreover, this phenomenon is closely relat-ed to coupling preferences. The results show that the influence of disassortative coupling is greatest, while the influence of assortative coupling is least.(2) We analyze the effect of network size on the robustness of interconnected network-s. Our results show that the robustness of interconnected networks is sensitive to the network size and the number of interconnected links. Wherein, when the two networks are coupled sparsely, the more similar the network sizes are, the more vulnerable the interconnected networks are; and when two network are coupled densely, the result is opposite. In addition, we also find that when two networks with different sizes are coupled, the larger one is more robust for sparse coupling, while more fragile for dense coupling.