Core-halo instability in dynamical systems

2013/02/13 by Seth Lloyd, Lloyd, Seth · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Complex Systems and Time Series Analysis #FOS: Physical sciences #nlin.CD

paper · pdf · doi:10.48550/arxiv.1302.3199

18 pages, 2 figures, latex

openalex publication_date 2013/02/13 · arxiv created 2015/12/15 · arxiv updated 2015/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper proves an instability theorem for dynamical systems. As one adds interactions between subystems in a complex system, structured or random, a threshold of connectivity is reached beyond which the overall dynamics inevitably goes unstable. The threshold occurs at the point at which flows and interactions between subsystems (`surface' effects) overwhelm internal stabilizing dynamics (`volume' effects). The theorem is used to identify instability thresholds in systems that possess a core-halo or core-periphery structure, including the gravo-thermal catastrophe -- i.e., star collapse and explosion -- and the interbank payment network. In the core-halo model, the same dynamical instability underlies both gravitational and financial collapse.

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• Theoretical investigations of an information geometric approach to complexity

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