Multiple Tipping Points and Optimal Repairing in Interacting Networks

ANTONIO MAJDANDZIC; LIDIA A. BRAUNSTEIN; CHESTER CURME; IRENA VODENSKA; SARY LEVY-CARCIENTE; H. E. STANLEY; SHLOMO HAVLIN

NATURE COMMUNICATIONS

Nature Publishing Group

Año: 2016 vol. 7

2041-1723

Systems composed of many interacting dynamical networks|such as the humanbody with its biological networks or the global economic network consisting of regional clusters often exhibit complicated collective dynamics. To understand the collective behavior of such systems, we investigate a model of interacting networks exhibiting the fundamental processes of failure, damage spread, and recovery. We find a very richphase diagram that becomes increasingly more complex as the number of interacting networks increases. In the simplest example of n = 2 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 pointsplay the dominant role in constructing the optimal repairing strategy in damaged interacting systems. To test our model, we analyze 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.