Abstract
In the real world, the construction of infrastructure networks is influenced by spatial factors. For such complex networks, We refer to them as spatial networks. This study investigates, based on the Bak–Tang–Wiesenfeld sandpile model, the impact of spatial factors on sandpile cascading avalanches. Through simulations, we discover that spatial factors not only facilitate the occurrence of moderate-scale avalanches in the system but also have a suppressing effect on the occurrence of the largest cascading avalanches. Using a multiplicative branching process, we analyze the influence of triangular structures composed of nodes on sandpile avalanches and find that nodes within triangular structures are relatively resistant to topples. Because of the relatively stable nature within triangular structures, more load tends to stay within this kind of structures. Once a cascading avalanche occurs in the system, the avalanche scale is often larger than that in the non-spatial counterpart. This increase in avalanche scale results in more load being released by the system, making the spatial networks more relaxed. And their probability of very-large-scale cascading avalanches is lower than that of non-spatial networks.
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