Multiple tipping points and optimal repairing in interacting networks

Antonio Majdandzic (), Lidia A. Braunstein, Chester Curme, Irena Vodenska, Sary Levy-Carciente, H. Eugene Stanley and Shlomo Havlin
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Antonio Majdandzic: Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
Lidia A. Braunstein: Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
Chester Curme: Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
Irena Vodenska: Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
Sary Levy-Carciente: Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
H. Eugene Stanley: Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
Shlomo Havlin: Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA

Nature Communications, 2016, vol. 7, issue 1, 1-10

Abstract: 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.

Date: 2016
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DOI: 10.1038/ncomms10850

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