Majdandzic, AntonioBraunstein, Lidia A.Curme, ChesterVodenska, IrenaLeyy-Carciente, SaryStanley, H. EugeneHavlin, Shlomo2019-11-132019-11-132016-03-01Antonio Majdandzic, Lidia A Braunstein, Chester Curme, Irena Vodenska, Sary Leyy-Carciente, H Eugene Stanley, Shlomo Havlin. 2016. "Multiple tipping points and optimal repairing in interacting networks." NATURE COMMUNICATIONS, Volume 7, 10850. https://doi.org/10.1038/ncomms108502041-1723https://hdl.handle.net/2144/38489Systems 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.This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/Financial networksComplex networksInterdependent networksArticle10.1038/ncomms108500000-0003-1183-7941 (Vodenska, Irena)52797