Simultaneous first- and second-order percolation transitions in interdependent networks

Dong Zhou, Amir Bashan, Reuven Cohen, Yehiel Berezin, Nadav Shnerb, and Shlomo Havlin
Phys. Rev. E 90, 012803 – Published 8 July 2014

Abstract

In a system of interdependent networks, an initial failure of nodes invokes a cascade of iterative failures that may lead to a total collapse of the whole system in the form of an abrupt first-order transition. When the fraction of initial failed nodes 1p reaches criticality p=pc, the abrupt collapse occurs by spontaneous cascading failures. At this stage, the giant component decreases slowly in a plateau form and the number of iterations in the cascade τ diverges. The origin of this plateau and its increasing with the size of the system have been unclear. Here we find that, simultaneously with the abrupt first-order transition, a spontaneous second-order percolation occurs during the cascade of iterative failures. This sheds light on the origin of the plateau and how its length scales with the size of the system. Understanding the critical nature of the dynamical process of cascading failures may be useful for designing strategies for preventing and mitigating catastrophic collapses.

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  • Received 4 October 2013
  • Revised 21 March 2014

DOI:https://doi.org/10.1103/PhysRevE.90.012803

©2014 American Physical Society

Authors & Affiliations

Dong Zhou1, Amir Bashan1, Reuven Cohen2, Yehiel Berezin1, Nadav Shnerb1, and Shlomo Havlin1

  • 1Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel
  • 2Department of Mathematics, Bar-Ilan University, Ramat Gan 52900, Israel

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Vol. 90, Iss. 1 — July 2014

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