Cascading Failures And Time Series Anylysis Based On Complex Theory

The rapid development of information technology makes human entered a new era of network, we already live in a complex network society. Complex network theory give us a network perspective on the problem. Researching on the topology of which abstracting from practical systems is an extremely important way to understand the relationship between different systems and their dynamic behavior. In this paper, we introduce the study of network topology from two aspects:the cascading failure of interdependent networks and time series analysis.The dependency among various infrastructure systems is more lightly in today’s society, which exchange more information and also make systems more fragile. Former studies on the robustness of isolate network can not embody the overall robustness of the network systems with dependencies. Thus, study of interdependent network robustness can accurately reflect the security and stability of those infrastructure systems. We first introduce the basic concept and study model of interdependent network, describe the current research status of interdependent network robustness. The topology of the network has a great influence on the dynamic behavior. Current studies mostly pay attention to the robustness of those interdependent networks consisted of two same structure networks. However, they didn’t consider the robustness of interdependent networks consisted of two different structure networks. Hence we take random attack strategy to study the robustness of interdependent networks with two different structure networks. We use three complex network model include random network, scale-free network and small world network, construct any two of them as interdependent networks. We find that interdependent networks with two different structure networks have richer properties about robustness. The interdependent networks consisted of WS small world network are extremely fragile under attack. Whereas interdependent networks consisted of NW small world network are more robust than other structure under attack. We further analysis relation between WS network’s reconnection probability and system’s robustness, and we observed that system’s robustness increase with reconnection probability increase. At the end of this part, the study of such interdependent networks robustness when initial attack different network was given. We consider that interdependent system’s robustness correlate with the structure of initial attacked network when under intentional attack but without any business with structure when under random attack.Another research of this paper is about time series analysis. Time series analysis has always been important research content in economic, hydrological, biological and other fields. Previous studies are based on mathematical or statistical method to analyze the time series. As the complex networks theory is becoming more mature, some people has developed method that can map time series to complex networks from this new angle. In this paper, we study logistic map sequence by mapping it to complex network using visibility graph method. We find that degree distribution of network generated by visibility graph can clearly distinguish period three and intermittent chaos. In order to explore more details about time series, we plot period-doubling bifurcation which color represent different node parameters. We observed some new dark line in period-doubling bifurcation figure which parameter is closeness centrality. Finally, we provide a simple new improved model based on visibility graph, which can effectively avoid the case that different time series is mapped to the same topological structure.