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Critical transitions in heterogeneous networks: Loss of low-degree nodes as an early warning signal

Alessandro Loppini, Simonetta Filippi, and H. Eugene Stanley
Phys. Rev. E 99, 040301(R) – Published 2 April 2019

Abstract

A large number of real networks show abrupt phase transition phenomena in response to environmental changes. In this case, cascading phenomena can induce drastic and discontinuous changes in the system state and lead to collapse. Although complex network theory has been used to investigate these drastic events, we are still unable to predict them effectively. We here analyze collapse phenomena by proposing a minimal two-state dynamic on a complex network and introducing the effect of local connectivities on the evolution of network nodes. We find that a heterogeneous system of interconnected components presents a mixed response to stress and can serve as a control indicator. In particular, before the critical transition point is reached a severe loss of low-degree nodes is observed, masked by the minimal failure of higher-degree nodes. Accordingly, we suggest that a significant reduction in less connected nodes can indicate impending global failure.

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  • Received 14 November 2018

DOI:https://doi.org/10.1103/PhysRevE.99.040301

©2019 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsNetworks

Authors & Affiliations

Alessandro Loppini1,*, Simonetta Filippi1,2,*, and H. Eugene Stanley3

  • 1Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, 00128 Rome, Italy
  • 2International Center for Relativistic Astrophysics Network–ICRANet, Piazza della Repubblica 10, Pescara I-65122, Italy
  • 3Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA

  • *Corresponding authors: a.loppini@unicampus.it; s.filippi@ unicampus.it

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Issue

Vol. 99, Iss. 4 — April 2019

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