title: Spatio-temporal propagation of cascading overload failures in spatially embedded networks.
abstract: 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.
authors.affiliation: School of Economics and Management, Beihang University, Beijing 100191, China.
authors.forename: Jichang
authors.initials: J
authors.lastname: Zhao
authors.affiliation: School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China.|Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing 100191, China.
authors.forename: Daqing
authors.initials: D
authors.lastname: Li
authors.affiliation: Department of Physics, Bar-Ilan University, Ramat Gan 5290002, Israel.
authors.forename: Hillel
authors.initials: H
authors.lastname: Sanhedrai
authors.affiliation: Department of Mathematics, Bar-Ilan University, Ramat Gan 5290002, Israel.
authors.forename: Reuven
authors.initials: R
authors.lastname: Cohen
authors.affiliation: Department of Physics, Bar-Ilan University, Ramat Gan 5290002, Israel.
authors.forename: Shlomo
authors.initials: S
authors.lastname: Havlin
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical; D062211:Spatio-Temporal Analysis