现代社会的运作越来越依赖于基础网络架构，并且由于子系统的衍生和系统之间的互连而变得越来越复杂。复杂网络上存在级联失效的风险，网络中部分节点的故障可能会由于节点间的相互连接关系引发网络中的其他节点的故障，这使得局部的故障可能引起一系列节点相继发生故障，最终导致网络中的大部分节点甚至整个网络失效。探究网络上的级联失效过程背后的机理对于保障网络顺利运行、提出应对级联失效的有效策略至关重要。
本文立足于复杂网络分析，运用Motter-Lai模型在网络上模拟级联失效过程，从级联失效后网络结构、级联失效过程中的时空特性、级联失效网络修复这三个角度入手，探索不同网络上级联失效过程的特征，发现级联失效后网络修复的过程存在的风险，为级联失效的事先预防、事后修复提供可靠的决策依据。本文主要工作如下：
1. 分别在无标度网络、规则网络和小世界网络上模拟了级联失效过程，分析级联失效对网络结构的影响。在无标度网络上，级联失效后网络仍然保持幂律度分布，当级联失效规模特别大的时候，网络度分布的拟合幂指数会显著增大，代表大度节点被更多地影响了。为了探究级联失效后网络能否保持原有特性，我们建立了与失效后网络性质相同的同规模网络作为对比。规则网络经过级联失效后，与同规模规则网络相比，平均距离变大，集聚系数略微减小。级联失效后的小世界网络与同规模小世界网络相比，集聚系数几乎不变，平均距离变小，网络仍然有小世界的特性。
2. 在二维晶格网基础上增加长程连边构造出有小世界特性的网络，分析空间嵌入式网络上级联失效的时空特征。本文采用了失效距离和基尼系数这两个定量化指标分别衡量故障在网络上传播的空间特征和传播的不均匀特性。结果显示，小世界网络上级联失效与规则网络上明显不同，故障在网络上传播的速度降低，故障传播的进程拉长，级联失效的规模减少，级联失效在小世界网络上出现长程扩散的现象。
3. 聚焦于级联失效后网络的修复过程，讨论修复策略存在的风险。研究发现，有的修复策略会触发进一步的级联失效，从而使得网络中最大连通集团的结构和功能反而受损。分别在无标度网络、规则网络和小世界网络失效后网络上测试修复不同节点后网络中触发级联失效的比例，以此测算不同网络中修复策略导致网络结构受损的风险程度。结果显示，无标度网络和小世界网络上，修复策略存在一定的风险，而规则网络上触发级联失效的风险更低。现实网络上修复节点触发级联失效的风险相比于模型网络上更高，这提醒我们，当我们将级联失效修复策略运用于现实网络中时，要警惕触发新的级联失效的潜在风险。

With the rapid development of science and technology, modern society has become increasingly dependent on the basic network, and network in real life become more and more complex due to the emergence of subsystems and the connection between systems. Cascading failure on networks is that localized failure may finally lead to catastrophes because of interactions between components in networks. Exploring the mechanism of cascading failure on networks is essential for ensuring operation of networks and proposing effective strategies to deal with the cascading failure.
Based on complex network analysis, we adopted the Motter-Lai model to simulate the cascading failure process on the network. In this paper, we focus on the three perspectives: the network structure after cascading failure, the spatiotemporal propagation of cascading overload failure, and the repair strategies after cascading failure. We finally have some insight into cascading failure on different networks and find potential risks in network repair process after the cascading failure. These conclusions in this paper provide a reliable decision basis for the prevention before and repair strategy after the cascading failure. This paper is mainly reflected in the following points:
1. We analyzed the influence of the cascade failure on the network structure by simulating cascading failure on scale-free networks, regular networks and small-world networks respectively. On a scale-free network, the degree distribution of network is still power-law distribution after cascading failure. When the cascading failure caused a catastrophe, the fitting power exponent of degree distribution will increase significantly, which means that a higher proportion of nodes with large degree failed. Compared with regular networks of the same scale, the average distance of regular networks after cascading failure becomes larger and the clustering coefficient is slightly reduced. Compared with small-world networks of the same scale and the same parameters, the average distance of small-world networks after cascading failure becomes smaller, the clustering coefficient is almost unchanged. In brief, the network is still a small-world network.
2. We constructed small-word networks based on the two-dimensional lattice network by adding long-range edges. Then we analyzed the spatiotemporal features of cascading failures on these spatial embedded networks. To measure the spatial features and the long-range propagation of cascading failure, we adopted two indicators that radius of failure and Gini coefficient. The results show that cascading failures on small-world networks are significantly different from regular networks. The speed of failure propagation on the network is reduced, but the duration is prolonged. On the meanwhile, the scale of cascading failures is reduced, and long-distance spread emerged on small-world networks.
3. It is found that some repair strategies will trigger new cascade failures, which will damage the structure and function of the giant component in the network. Considering that network structures after cascading failures are different due to the different kind of the original networks, we tested the nodes repair strategy on the scale-free networks, regular networks, and small-world networks respectively. The proportion of causing further cascade failures is used to measure the risk caused by the repair strategy in different networks. The results show that the repair process is indeed risky. There is a relatively low risk of repair process on regular networks compared to the other model network. The risk of repair process on the real network is higher than that on the model network. It reminds us that we must be alert to the possibility of danger in repair process, especially when we apply the cascading failure repair strategy to real networks.