Different from the direct contact in epidemics spread, overload failures propagate through hidden functional dependencies. Many studies focused on the critical conditions and catastrophic consequences of cascading failures. However, to understand the network vulnerability and mitigate the cascading overload failures, the knowledge of how the failures propagate in time and space is essential but still missing. Here we study the spatio-temporal propagation behaviour of cascading overload failures analytically and numerically on spatially embedded networks. The cascading overload failures are found to spread radially from the centre of the initial failure with an approximately constant velocity. The propagation velocity decreases with increasing tolerance, and can be well predicted by our theoretical framework with one single correction for all the tolerance values. This propagation velocity is found similar in various model networks and real network structures. Our findings may help to predict the dynamics of cascading overload failures in realistic systems.
|State||Published - 12 Jan 2016|
Bibliographical noteFunding Information:
We thank the support from Collaborative Innovation Center for industrial Cyber-Physical System. D.L. is also supported by the National Natural Science Foundation of China (Grant 61104144) and the National Basic Research Program of China (2012CB725404). S.H. thanks DTRA, ONR, the LINC and the Multiplex (No. 317532) EU projects, the DFG, and the Israel Science Foundation for support. J.Z. was partially supported by NSFC (Grant Nos 71501005 and 71531001) and 863 Program (Grant No. SS2014AA012303).