Multiple Tipping Points and Optimal Repairing in Interacting Networks

TL;DR

This paper models interacting networks to understand failure, damage spread, and recovery, revealing complex phase diagrams and the importance of triple points in optimal repair strategies, supported by real financial network analysis.

Contribution

It introduces a detailed model of interacting networks with complex phase behavior, highlighting the role of triple points in repair strategies, and validates findings with real financial data.

Findings

Rich phase diagram with multiple critical and triple points

Triple points are key to optimal repair strategies

Empirical evidence from financial networks supports the model

Abstract

Systems that comprise 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. 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 rich phase diagram that becomes exponentially more complex as the number of networks is increased. In the simplest example of $n=2$ interacting networks we find two critical points, 4 triple points, 10 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 support 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.