Universal behavior of cascading failures in interdependent networks

Dongli Duan, Changchun Lv, Shubin Si, Zhen Wang, Daqing Li, Jianxi Gao, Shlomo Havlin, H. Eugene Stanley, Stefano Boccaletti

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73 Scopus citations


Catastrophic and major disasters in real-world systems, such as blackouts in power grids or global failures in critical infrastructures, are often triggered by minor events which originate a cascading failure in interdependent graphs. We present here a self-consistent theory enabling the systematic analysis of cascading failures in such networks and encompassing a broad range of dynamical systems, from epidemic spreading, to birth–death processes, to biochemical and regulatory dynamics. We offer testable predictions on breakdown scenarios, and, in particular, we unveil the conditions under which the percolation transition is of the first-order or the second-order type, as well as prove that accounting for dynamics in the nodes always accelerates the cascading process. Besides applying directly to relevant real-world situations, our results give practical hints on how to engineer more robust networked systems.

Original languageEnglish
Pages (from-to)22452-22457
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number45
StatePublished - 5 Nov 2019

Bibliographical note

Publisher Copyright:
© 2019 National Academy of Sciences. All rights reserved.


ACKNOWLEDGMENTS. This work was supported by National Natural Science Foundation of China Projects U1803263, 71401178, 71771186, and 71631001; National 1000 Young Talent Plan W099102; China Postdoctoral Science Foundation Project n.2017M613336; and Natural Science Foundation of Shaanxi Province Project n.2017JM7011. J.G. was partially supported by Knowledge and Innovation Program Grant 1415291092 at Rensselaer Polytechnic Institute and Office of Naval Research (ONR) Contract N00014-15-1-2640; S.H. acknowledges financial support from the Israel Science Foundation (ISF), ONR Grant N62909-14-1-N019, Defense Threat Reduction Agency (DTRA) Grant HDTRA-1-10-1-0014, BSF-NSF 2015781, Israel Ministry of Science and Technology with the Italian Ministry of Foreign Affairs and the Army Research Office; H.E.S. acknowledges the support from NSF Grant PHY-1505000 and DTRA Grant HDTRA1-14-1-0017 for the Boston University Center for Polymer Studies. We also thank Xueming Liu for useful discussions.

FundersFunder number
Italian Ministry of Foreign Affairs and the Army Research OfficePHY-1505000, HDTRA1-14-1-0017
Office of Naval ResearchN00014-15-1-2640
Defense Threat Reduction AgencyBSF-NSF 2015781, HDTRA-1-10-1-0014
Rensselaer Polytechnic Institute
Boston University
Iowa Science FoundationN62909-14-1-N019
National Natural Science Foundation of ChinaU1803263, 71771186, 71631001, 71401178
China Postdoctoral Science Foundation2017M613336
Israel Science Foundation
Ministry of science and technology, Israel
Natural Science Foundation of Shaanxi Province1415291092, 2017JM7011


    • Cascading failure
    • Interdependent network
    • Robustness
    • Spreading


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