Reviving a failed network through microscopic interventions

TL;DR

This paper introduces a two-step recovery method for complex networks that combines topological reconstruction with targeted dynamic interventions to revive systems stuck in undesirable states.

Contribution

It presents a novel framework for identifying recoverable phases in complex networks and guides effective microscopic interventions for system revival.

Findings

Identifies the recoverable phase where minimal interventions suffice

Maps boundaries of the recoverable phase in complex systems

Demonstrates successful revival through microscopic control

Abstract

From mass extinction to cell death, complex networked systems often exhibit abrupt dynamic transitions between desirable and undesirable states. Such transitions are often caused by topological perturbations, such as node or link removal, or decreasing link strengths. The problem is that reversing the topological damage, namely retrieving the lost nodes or links, or reinforcing the weakened interactions, does not guarantee the spontaneous recovery to the desired functional state. Indeed, many of the relevant systems exhibit a hysteresis phenomenon, remaining in the dysfunctional state, despite reconstructing their damaged topology. To address this challenge, we develop a two-step recovery scheme: first - topological reconstruction to the point where the system can be revived, then dynamic interventions, to reignite the system's lost functionality. Applying this method to a range of nonlinear network dynamics, we identify the recoverable phase of a complex system, a state in which the system can be reignited by microscopic interventions, for instance, controlling just a single node. Mapping the boundaries of this dynamical phase, we obtain guidelines for our two-step recovery.