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Europhysics Letters 108 (2014) 56002
Cascading failures on networks
with asymmetric dependence
Ming Li, Run-Ran Liu , Chun-Xiao Jia and Bing-Hong Wang
Networks with mutual dependence have been shown to be much more vulnerable to random failures and targeted attacks than those without. However, in real networks, the dependence between two nodes is not always mutual. Periphery nodes may depend on hub nodes, yet the converse is not necessarily true. Considering this asymmetric dependence, we propose a model of cascading dynamics of networks, where the dependence between nodes is determined by their degrees. We find that the asymmetric dependence makes networks more robust than the symmetric one, and the percolation transition point is not sensitive to the number of the asymmetric dependence nodes. Furthermore, scale-free networks with asymmetric dependence can still be very robust to random failures, rather than extremely fragile as the one with mutual dependence. We also develop an approach to analyse this model and obtain the exact solution for the size of the giant component and the critical point. Both simulation and analytical results reveal the existence of the crossover between the first- and the second-order percolation transitions in our model.
含非对称相依关系网络之级联故障研究
近年来,考虑到系统间或系统内的结构与功能的依赖特性,含相依节点的网络的级联故障得到了广泛的研究。这些研究表明,由于网络中节点的相互依赖,网络变得极脆弱,很容易被外界攻击所完全摧毁。而我们注意到这些研究中都假设依赖是对称的,即两个节点互相依赖。但是,真实系统中的依赖并不是总是相互的,外围节点会依赖于hub节点,而hub节点并不会依赖外围节点。因此,我们研究了不对称依赖对网络级联故障的影响。在我们的模型中,一个小度节点会依赖于一个大度节点,而大度节点并不一定会依赖于这个小度节点。研究发现,这种不对称依赖性不同于相互依赖,它并不会使网络变得极其脆弱,并且网络逾渗相变的临界点也对这种不对称依赖节点量的变化不敏感。我们知道,面对随机故障时,相互依赖使得无标度网络变得比随机网络更脆弱,且度分布越宽网络越脆弱。但是,在不对称依赖的情况下,无标度网络依然比随机网络更鲁棒,这一现象也更符合实际。此外,我们也对模型进行了解析与相变分析,发现了系统中存在一阶与二阶两种相变过程,且与模拟结果完全吻合。论文发表于(EPL, 2014, 108(5): 56002)
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EPL.108(2014)56002LiLiuJiaWang.pdf
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