Many complex networks in real life are embedded in space and most infrastructure networks are interdependent, such as the power system and the transport network. In this paper, we construct two cascading failure models on the multilayer spatial network. In our research, the distance l between nodes within the layer obeys the exponential distribution P ( l ) ∼ exp(– l / ζ ), and the length r of dependency link between layers is defined according to node position. An entropy approach is applied to analyze the spatial network structure and reflect the difference degree between nodes. Two metrics, namely dynamic network size and dynamic network entropy, are proposed to evaluate the spatial network robustness and stability. During the cascading failure process, the spatial network evolution is analyzed, and the numbers of failure nodes caused by different reasons are also counted, respectively. Besides, we discuss the factors affecting network robus...

中文翻译：

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多层空间网络中基于过载的级联失效分析

现实生活中许多复杂的网络都嵌入在空间中，并且大多数基础结构网络是相互依赖的，例如电力系统和传输网络。在本文中，我们在多层空间网络上构建了两个级联故障模型。在我们的研究中，层内节点之间的距离l服从指数分布P（l）〜exp（– l /ζ），并且层间依赖链接的长度r根据节点位置定义。运用熵的方法分析空间网络结构，反映节点之间的差异程度。提出了两个指标，即动态网络规模和动态网络熵，以评估空间网络的鲁棒性和稳定性。在级联故障过程中，分析了空间网络的演化，并分别计算了由于不同原因导致的故障节点数量。此外，我们讨论了影响网络稳定性的因素。