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Multiple tipping points and optimal repairing in interacting networks

Author

Listed:
  • Antonio Majdandzic

    (Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA)

  • Lidia A. Braunstein

    (Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
    Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Universidad Nacional de Mar del Plata-CONICET)

  • Chester Curme

    (Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA)

  • Irena Vodenska

    (Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
    Metropolitan College, Boston University)

  • Sary Levy-Carciente

    (Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
    Economics and Social Sciences Faculty, Central University of Venezuela)

  • H. Eugene Stanley

    (Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA)

  • Shlomo Havlin

    (Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
    Bar-Ilan University)

Abstract

Systems composed of many interacting dynamical networks—such as the human body with its biological networks or the global economic network consisting of regional clusters—often exhibit complicated collective dynamics. Three fundamental processes that are typically present are failure, damage spread and recovery. Here we develop a model for such systems and find a very rich phase diagram that becomes increasingly more complex as the number of interacting networks increases. In the simplest example of two interacting networks we find two critical points, four triple points, ten allowed transitions and two ‘forbidden’ transitions, as well as complex hysteresis loops. Remarkably, we find that triple points play the dominant role in constructing the optimal repairing strategy in damaged interacting systems. To test our model, we analyse an example of real interacting financial networks and find evidence of rapid dynamical transitions between well-defined states, in agreement with the predictions of our model.

Suggested Citation

  • Antonio Majdandzic & Lidia A. Braunstein & Chester Curme & Irena Vodenska & Sary Levy-Carciente & H. Eugene Stanley & Shlomo Havlin, 2016. "Multiple tipping points and optimal repairing in interacting networks," Nature Communications, Nature, vol. 7(1), pages 1-10, April.
  • Handle: RePEc:nat:natcom:v:7:y:2016:i:1:d:10.1038_ncomms10850
    DOI: 10.1038/ncomms10850
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    Cited by:

    1. Gurami Tsitsiashvili, 2021. "Study of Synergistic Effects in Complex Stochastic Systems," Mathematics, MDPI, vol. 9(12), pages 1-14, June.
    2. Michael M. Danziger & Albert-László Barabási, 2022. "Recovery coupling in multilayer networks," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    3. Zhong, Jilong & Zhang, FengMing & Yang, Shunkun & Li, Daqing, 2019. "Restoration of interdependent network against cascading overload failure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 884-891.
    4. Gangwal, Utkarsh & Singh, Mayank & Pandey, Pradumn Kumar & Kamboj, Deepak & Chatterjee, Samrat & Bhatia, Udit, 2022. "Identifying early-warning indicators of onset of sudden collapse in networked infrastructure systems against sequential disruptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    5. Wang, Shuliang & Gu, Xifeng & Luan, Shengyang & Zhao, Mingwei, 2021. "Resilience analysis of interdependent critical infrastructure systems considering deep learning and network theory," International Journal of Critical Infrastructure Protection, Elsevier, vol. 35(C).
    6. Irena Vodenska & Hideaki Aoyama & Yoshi Fujiwara & Hiroshi Iyetomi & Yuta Arai, 2016. "Interdependencies and Causalities in Coupled Financial Networks," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-32, March.

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