Sandpile cascades on interacting tree-like networks
arXiv (Cornell University)(2010)
摘要
The vulnerability of an isolated network to cascades is fundamentally
affected by its interactions with other networks. Motivated by failures
cascading among electrical grids, we study the Bak-Tang-Wiesenfeld sandpile
model on two sparsely-coupled random regular graphs. By approximating
avalanches (cascades) as a multi-type branching process and using a
generalization of Lagrange's expansion to multiple variables, we calculate the
distribution of avalanche sizes within each network. Due to coupling, large
avalanches in the individual networks are mitigated--in contrast to the
conclusion for a simpler model [36]. Yet when compared to uncoupled networks,
interdependent networks more frequently suffer avalanches that are large in
both networks. Thus sparse connections between networks stabilize them
individually but destabilize them jointly, as coupling introduces reservoirs
for extra load yet also inflicts new stresses. These results suggest that in
practice, to greedily mitigate large avalanches in one network, add connections
between networks; conversely, to mitigate avalanches that are large in both
networks, remove connections between networks. We also show that when only one
network receives load, the largest avalanches in the second network increase in
size and in frequency, an effect that is amplified with increased coupling
between networks and with increased disparity in total capacity. Our framework
is applicable to modular networks as well as to interacting networks and
provides building blocks for better prediction of cascading processes on
networks in general.
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关键词
avalanches,sandpile models,02.50.ey.,64.60.aq,branching processes,cascades,random graphs,modular networks,self-organized criticality. pacs: 89.75.hc,branching process,interaction network,neural network,random graph
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