| Cascading failures commonly occur in many complex networked systems on which modern societies very much depend, such as communication network, traffic network, power grid network, water supply network, gas supply network, etc. In recent years, various disasters induced by large-scale cascading failures have taken place again and again, which have had great and extremely negative impact on national economy and social development. Benefiting from the need of understanding and controlling these disasters, cascading failures on complex networks have been received a wide range concerns by scholars at home and abroad. Based on existing research fruits, this thesis analyzes deeply and models theoretically cascading failures on complex networks from the angle of complex networks theory and networks with new and different reality scenes, and closely focusing on flow dynamics process which is closely related to the occurrence and propagation of cascading failure, and investigates dynamical properties of cascading failures through measures to the network robustness against cascading failures, which provide the basis to develop reasonable and effective protection strategies for the networks. The main results of the thesis are as follows:1. Aiming at cascading failures on complex networks subject to attacks, and considering that the attack information may be incompletely precise and edge-to-node failure mode, a cascading model based on grey information is proposed. The accuracy of information can be controlled by a tunable parameter, the random and intentional attack are two extreme cases of the model. Cascades of node failures triggered by edge attacks on two typical model networks are investigated, and the effect of the parameter about information for the different networks robustness against cascading failures is analyzed and among which the critical phenomenon is found, and the two important factors:information conditions and dynamic characteristics of the network determining the network robustness are revealed.2. Considering the flow governed by the natural laws to model distributed flow which is ubiquitous in real networks, and using a load-capacity relation which is more suitable for real networks, a cascading model with a tunable weight parameter is proposed on the basis of distributed flow. Cascading failures on typical weighted both model networks and real network subject to deliberate attacks on node and edge are investigated. The different optimal parameter values corresponding to the strongest robustness achievement for the networks respectively against cascades of node and edge failures are obtained. Moreover, by comparing with previous shortest-path flow strategy from further simulation and empirical analysis, we find that whether it is against cascades of node failures or edge failures, distributed flow strategy which does not require global information of network topology makes the networks more robust, more reducing significantly the possibility of the occurrence of the cascading failure dynamics.3. To better explore the robustness against cascading failures on weighted networks, a betweenness-dependent node weighting scheme is proposed, and a cascading model with a tunable weight parameter is constructed by applying the local weighted flow redistribution rule. Cascading failures triggered by small node attacks on various weighted networks are studied. The numerical simulation and theoretical analysis results give a value of the weight parameter corresponding to the strongest robustness achievement for the studied four typical model networks. Furthermore, compared with existing degree-dependent strategy, the betweenness-dependent weighting strategy makes the networks more robust, showing that the possibility of the occurrence of the cascading failure and the size of the cascade in case of occurrence are more reduced. The effectiveness of this result is demonstrated by empirical studies for four real networks.4. Under the background of communication networks, and considering that it is difficult to acquire global information about network congestion, a routing strategy with a tunable parameter is proposed on the basis of local congestion information, and a cascading model is constructed by introducing a packet-hopping model incorporating the birth-death process and considering a failure mechanism for overloaded nodes. According to new measures to the robustness of a network against cascading failures, cascading failures on typical model networks triggered by deliberate node attacks are investigated, the effect of the routing parameter, time delay about congestion information, packet generation rate, network topology for the network robustness is analyzed, the existence of optimal values of the routing parameter corresponding to the strongest robustness achievement for the networks is found. Furthermore, the local routing is extended to a global (unfeasible) routing, and the correlation between the finiteness for congestion information and the network robustness is studied, and some valuable results are obtained. |
