Multiple tipping points and optimal repairing in interacting networks
Abstract
Systems composed of many interacting dynamical networkssuch as the human body with its biological networks or the global economic network consisting of regional clustersoften 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 welldefined states, in agreement with the predictions of our model.
 Publication:

Nature Communications
 Pub Date:
 March 2016
 DOI:
 10.1038/ncomms10850
 arXiv:
 arXiv:1502.00244
 Bibcode:
 2016NatCo...710850M
 Keywords:

 Physics  Physics and Society;
 Condensed Matter  Statistical Mechanics
 EPrint:
 7 figures, typos corrected, references added