Network structural origin of instabilities in large complex systems

TL;DR

This paper investigates how structural properties of large directed networks, such as imbalances in links and paths, lead to nonnormality and reactivity, affecting their stability and response to perturbations.

Contribution

It identifies key structural features causing nonnormality and reactivity in real networks and develops a predictive theory for these phenomena.

Findings

Imbalances in links and paths cause nonnormality and reactivity.

A quantitative theory predicts network stability responses.

Results can inform network design and control strategies.

Abstract

A central issue in the study of large complex network systems, such as power grids, financial networks, and ecological systems, is to understand their response to dynamical perturbations. Recent studies recognize that many real networks show nonnormality and that nonnormality can give rise to reactivity--the capacity of a linearly stable system to amplify its response to perturbations, oftentimes exciting nonlinear instabilities. Here, we identify network structural properties underlying the pervasiveness of nonnormality and reactivity in real directed networks, which we establish using the most extensive data set of such networks studied in this context to date. The identified properties are imbalances between incoming and outgoing network links and paths at each node. Based on this characterization, we develop a theory that quantitatively predicts nonnormality and reactivity and explains the observed pervasiveness. We suggest that these results can be used to design, upgrade, control, and manage networks to avoid or promote network instabilities.