Abstract: There are a large number of directed networks in the real world. According to a directional edge in the network, a cascading failure model was proposed which is suitable to describe the coupled map lattices with directed network. In this paper, using simulation methods, the cascading failures with BA (Barabási-Albert) scale free and ER (Erds-Rényi) random graph directed networks in this model was researched. Two attack strategies: deliberate attack and random attack were adopted in this fixed node number network, and relevant data were recorded. By analyzing the data, following conclusions can be made: 1) the cascading failures are much easier to occur in directed network than in undirected network; 2) when the networks are attacked, directed networks are more vulnerable than undirected networks; 3) in ER random graph networks, there is linear relationship among four thresholds with fault size increasing when network faults occur.

Key words: directed network, couple map lattices, cascading failure, complex network

摘要： 针对现实世界中存在大量的有向网络，根据有向网络中边的有向性，提出适合描述有向网络耦合映像格子（CML）的相继故障模型，利用仿真分析的方法研究了BA无标度有向网络和ER随机图有向网络在该模型作用下的相继故障行为。仿真中，对节点数固定的网络采用蓄意攻击和随机攻击两种策略进行攻击，并记录相关数据。通过对所得数据的分析发现：1）这两类有向网络的相继故障进程比同规模的无向网络要剧烈；2）当网络遭受攻击时，有向网络比无向网络更加脆弱；3）ER随机图网络相继故障发生过程中引起网络相继故障规模增长的4个临界值之间存在线性关系。

关键词: 有向网络, 耦合映像格子, 相继故障, 复杂网络