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Instability in Complex Oscillator Networks: Limitations a...
[Submitted on 27 Feb 2024 (v1), last revised 17 Jul 2026 (this v · 2024-02-27 · via cs.LG updates on arXiv.org

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Abstract:A central question of network science is how functional properties of systems emerge from their structure. For networked dynamical systems, structure is typically captured through network measures. We investigate the relationship between these measures and stability metrics across non-linear and linear oscillators, as well as real-world power grid topologies and dynamics. We find that this relationship is highly sensitive to the underlying ensemble: minor changes in the networks considered, such as going from mean degree 6 to mean degree 8, can invert the correlation between a network measure and stability. We also investigate network measures as inputs for machine learning, as well as Graph Neural Networks (GNNs) as predictors of stability. Both GNNs and the non-linear combination of many network measures can accurately predict stability within a given ensemble, yet both can fail when the ensemble changes. We conclude that neither approach reliably identifies the underlying structural causes of instability.

Submission history

From: Christian Nauck [view email]
[v1] Tue, 27 Feb 2024 13:34:08 UTC (10,486 KB)
[v2] Fri, 17 Jul 2026 12:25:14 UTC (3,947 KB)