Study On Robustness Of Coupled Interdependent Networks Under Attacks

As an important branch of complexity theory, complex networks theory attracts more and more scholars from various research. With rapid growth of information technologies, empirical data are getting increasingly rich. Based on the quantitative analysis of big data, theoretical research, algorithm design, practical application, and platform framework etc., the study of complex networks has flourished over the past few years. Previous studies mainly concentrated on the innovation of theory and method of isolated network. However, most real networks are coupled as interdepen-dent networks. Therefore, the study has some theoretical and practical significance. In this thesis, according to the coupling characteristics in real networks, we classify the coupling dependency networks into four categories:I) there only exist interdependendy links, II) there exist support-dependence links between networks, III) there exist only interconnectivity links, IV) there exist interdependent and interconnect links. When the system are under random attack or targeted attack, we study the robustness of networks with theoretical and simulating analysis, by considering the nodes failure mechanisms of internal network and between two networks.1Random attack on coupled interdependent networks(1) For the robustness of partially coupled clustered networks with multiple support-dependence relations under random attack, we find that, for strong coupling strength, clustering coefficient has a significant impact on the robustness of the system, but for weak coupling strength, it has little effect especially when attacking the both two networks. By defining the functional nodes in the network of networks (NON) and developing the analytical framework, we study the robustness of NON with multiple support-dependence relations under random attack. The system will be more robust by increasing the fraction of autonomous nodes, and the density of support links.(2) We study the robustness of two interdependent and interconnected networks with feedback condition under random attack based on the percolation theory. We find that increasing the coupling strength leads to a change from a second to first through hybrid order percolation transition. As the average interconnectivity links degree increases, the first order transition region grows large, the hybrid order transition region becomes small and ultimately disappears. And as the average intralinks degree increases, the first order transition region becomes small, the second order transition region becomes large, and the hybrid order transition region remains unchanged. Additionally, we study the robustness of interdpendent and interconnected network of networks (NON) with feedback condition or no feedback condition under random attack. For a starlike network of Erdos-Renyi (ER) networks, we find that the central network becomes more vulnerable as the number of networks increase, and becomes more robust as the average inter-or intra-connectivity links degree increases. Especially when the coupling strength is equal to one, we get the analytical expression of the first order critical point. Comparing to no feedback case,the feedback condition makes the system more vulnerable. Our theory is not only applied to random network, but also applied to any network systems topology.2Targeted attack on coupled interdependent networks(1) We study the robustness of two partially interdependent networks under targeted attack analytically and numerically. A new targeted probability function with parameter a is introduced. When a=0,1, we obtain the analytical solutions of critical points from first to second order phase transition. The robustness of partially interdependent network of networks (NON) is also studied. When highly connected nodes have higher probability to fail, the system becomes more vulnerable. For a fully interdependent treelike network of ER networks, we get the analytical solutions of the giant component and the critical threshold pc. For a part-ially interdependent starlike network of ER networks, as the number of networks increases, the central network becomes more vulnerable.(2) We study the robustness of two interdependent and inter conne-cted networks with feedback condition or no feedback condition under targeted attack. We find from numerical simulation that, when highly con-nected nodes have high probability to fail,the system becomes more vulnerable. But when low connected nodes have high probability to fail, the system becomes more robust. Furthermore, we study the robustness of network of networks (NON) with multiple support-dependence relations under targeted attack. Besides increasing the fraction of autonomous nodes, and the density of support links, we can still improve the robustness of networks by protecting the nodes with higher degree.