Spreading of localized attacks in spatial multiplex networks

Dana Vaknin, Michael M. Danziger, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


Many real-world multilayer systems such as critical infrastructure are interdependent and embedded in space with links of a characteristic length. They are also vulnerable to localized attacks or failures, such as terrorist attacks or natural catastrophes, which affect all nodes within a given radius. Here we study the effects of localized attacks on spatial multiplex networks of two layers. We find a metastable region where a localized attack larger than a critical size induces a nucleation transition as a cascade of failures spreads throughout the system, leading to its collapse. We develop a theory to predict the critical attack size and find that it exhibits novel scaling behavior. We further find that localized attacks in these multiplex systems can induce a previously unobserved combination of random and spatial cascades. Our results demonstrate important vulnerabilities in real-world interdependent networks and show new theoretical features of spatial networks.

Original languageEnglish
Article number073037
JournalNew Journal of Physics
Issue number7
StatePublished - Jul 2017

Bibliographical note

Publisher Copyright:
© 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.


  • complex systems
  • percolation theory
  • phase transitions
  • spatial multiplex networks


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