Analysis of overload-based cascading failure in multilayer spatial networks

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 distancelbetween nodes within the layer obeys the exponential distributionP(l) similar to exp(-l/zeta), and the lengthrof 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 robustness. Simulations demonstrate that the larger the values of average degree < k & rang;, the stronger the network robustness. As the lengthrdecreases, the network performs better. When the probabilitypis small, as zeta decreases, the network robustness becomes more reliable. Whenpis large, the network robustness manifests better performance as zeta increases. These results provide insight into enhancing the robustness, maintaining the stability, and adjusting the difference degree between nodes of the embedded spatiality systems.