Network structural origin of instabilities in large complex systems

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.

arXiv commentIncludes Supplementary Materials

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• The Efficiency of Synchronization Dynamics and the Role of Network Syncreactivity
• Broken detailed balance and entropy production in directed networks
• Strong Connectivity in Real Directed Networks
• "Layer-by-layer" Unsupervised Clustering of Statistically Relevant Fluctuations in Noisy Time-series Data of Complex Dynamical Systems
• Persistence of chimera states and the challenge for synchronization in real-world networks
• Dynamics in non-Hermitian systems with nonreciprocal coupling
• The Spectral Boundary of Block Structured Random Matrices
• Data-driven assessment of optimal spatiotemporal resolutions for information extraction in noisy time series data
• Single-Integrator Consensus Dynamics over Minimally Reactive Networks
• Disorder-promoted stability