Research On The Mechanism Of Cascading Dynamics And Behaviors Of Complex Networks

Modern society increasingly relies on network infrastructures that include the power grids, communication networks, Internet, computer networks, financial networks and traffic networks. As the netware-based degree improves, the function of network infrastructures becomes more and more powerful and the overall efficiency of network systems has been greatly enhanced. However, the interdependence and interconnection among networks is increasing and the internal dynamics of networks has become more complex. As a result, all of these facts increase the possibility of collapse in network systems. When the networks are subjected to many kinds of external or internal disasters and threats, such as the extreme weather, malicious attacks and disruptions, artificial misoperations and random faults, it will lead to serious consequences. Even a small abnormal event, through cascade, will spread through the whole network systems and result in large-scale collapse. From the aspect of dynamics, the process of conductivity is called as "Cascading Failures".The cascading failures or disasters emerged frequently in networks always destroyed the systems, caused the interruption of service, severely threatened the safe running of infrastructure networks and caused huge economic loss. Therefore, under the conditions of network attacks, serious accidents, human negligence and random breakdown and so on, the network security or survivability resulting from reckoning behavior and cascading failures has attracted great attention of many countries and the governments. Especially, the United States and Europe, as the representatives of the developed countries, have raised the focus on the network survivability anti-destroying ability to national strategy plan. At the same time, it has become the front and hotspot in area of the network security. At present, the research on network security resulting from cascading behaviors mainly focuses on the robustness of network topological structures and the results of cascading failures. However, there is lack of attention to the evolutional process of cascading dynamics. Especially, for the evolutional rules and characteristics of cascade events showed in different stages from emerging, developing, oscillating and outbreaking, there is lack of understanding.From the aspect of dynamics, this work breaks through the limitations of previous research, takes "the cascading dynamics and behaviors of complex networks" as the core and focuses on the evolution process of cascading failures. Combining the statistical analysis with comparative analysis and following the steps from studying the network models constructed to studying to the empirical analysis of the steps, this work starts from the main factors of inducing the cascading failures including the internal and external factors, and then investigates the process of the dynamics, the evolution rules and characteristics for network collapse. The main research is listed below. Firstly, we reveal the lifecycle of cascading failures and the time features of broken components of networks in the cascading process. Secondly, we dig out the vulnerable nodes and vulnerable links in cascading process by exploring the inner relationship between the, vulnerability of network components and the broken form of networks. Thirdly, induced by different attacks on the links in networks, we investigate the process of cascading dynamics with emergent recovery mechanism to optimize the schedule and configuration of limited external resources. The work can provide the important theory for emergent response and control of cascading failures under the major disaster.The main innovation points of this work are as followed:(1) This work explores the life cycle of the cascading failures and the time features of broken components of networks in the cascading process. We study the process of cascading dynamics induced by attacking the nodes and the links in networks, respectively. As a result, we find that, under both intentional attack and random breakdown, the life cycle of cascade in Scale-free networks is always longer than that both in ER random networks and WS small-world networks. Under the intentional attack, the number of the avalanche edges or nodes in both WS small-world networks and ER random networks always reach a peak over a period of time. Under node-targeted attack, most of the avalanche nodes in Scale-free networks always occur at the beginning of the cascading failures. While under random breakdown, most of the avalanche nodes or links in Scale-free, WS small-world and ER networks always occur at the beginning of the cascading failures as the nodes and links have high tolerance. The results have great significance for protecting key infrastructure networks.(2) This work probes the inner relationship between the vulnerability of the links and the cascading failures in networks in order to identify the vulnerable links in cascading propagation. For the question that how to identify the vulnerable links in networks, we model the cascading dynamics for the physical load assigned to the edges in networks and define four kinds of weighting methods to characterize the features of the edges. The feature of the avalanche edges in cascading propagation is investigated under various attacking strategies. We find that, as the links have weak tolerance, for Scale-free, WS and ER networks under both intentional attack and random breakdown, the links with small product of betweenness centrality of its two ends will be vulnerable and they have the highest proportion of the avalanche links. On the other hand, as the links have high tolerance, under random breakdown, the links with high product of betweenness centrality of its two ends will be vulnerable. The results verify the known "barrel principle" again. The results will be important for analyzing the potential safety problems and protecting the networks with the load assigned to the links.(3) This work probes the inner relationship between the vulnerability of the nodes and the cascading failures in networks in order to identify the vulnerable nodes in cascading propagation. For the question that how to identify the vulnerable nodes in networks, we modeled the cascading dynamics for the physical load assigned to the nodes in networks and defined four kinds of weighting methods to characterize the features of the nodes. The feature of the avalanche nodes in cascading propagation is investigated under various attacking strategies on nodes. We find that, for Scale-free networks under intentional attack, the nodes with small value for the fourth kind of weighting method are vulnerable. The numerical simulations of the real network with scale-free characteristics verify the findings; While for WS small-world and ER networks under intentional attack, as the nodes have weak tolerance, the nodes with high degree and small value for the fourth weight are vulnerable. On the other hand, under random breakdown, the nodes with high degree will be vulnerable. The results will be important for analyzing the potential safety problems and protecting the networks with the load assigned to the nodes.(4) With limited external resources, the emergency strategy of the response of the cascading failures induced by the attacks on the links in networks is presented. In fact, it needs to optimize the resource configuration according to the difference of safety ability among the individuals. Therefore, for the Scale-free networks with power-law degree distribution, under the condition of limited resources, we present the emergency response of the cascading failures induced by edge-based attack, in which, we optimize the resources according to the characteristics of edges in order to improve the ability of dealing with the failures. As a result, as the external resources are deployed to the edges according to the fourth kind of strategy, the external resources can effectively maintain network connectivity, control the velocity of the cascade propagation and control the outbreak of collapse in network. Then, the further numerical simulations of the real networks with scale-free characteristics verify the results.To sum up, this work reveals the evolution rules and the features of cascading dynamics in the cascade process, which provides the important theory for protecting the safe running of the infrastructure networks such as the power grids, transportation networks, telecommunication networks and Internet. At the same time, in the situation of open, complex and dynamical environment, this work also provides new theory and method for research on both the network behavior security induced by abnormal behaviors and information security based on network thinking.