Quantifying the irregularity of a time series

2025/11/25 by Max Potratzki, Manuel Adams, Timo Bröhl +1 · 1 voice
Physics and Astronomy · #nlin.CD #physics.data-an

paper · pdf · doi:10.1103/3vzd-7kg2

Abstract

We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition network derived from a time series. We demonstrate numerically that circulance sensitively and robustly positions time series of canonical model systems, representative of preset dynamical regimes, along a continuous spectrum from regularity to randomness. Analyzing empirical data from long-term observations of high-dimensional, complex systems -- human brain and the Sun -- reveals that circulance aids in elucidating different dynamical regimes.

Citations

• Deep learning for classifying dynamical states from time series via recurrence plots
• Bistability in the sunspot cycle
• Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks
• Characterizing stochastic time series with ordinal networks
• A Look into Chaos Detection through Topological Data Analysis
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• Conditional entropy of ordinal patterns
• Extreme events in excitable systems and mechanisms of their generation
• Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods
• Description of stochastic and chaotic series using visibility graphs
• Horizontal visibility graphs: exact results for random time series
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• From time series to complex networks: The visibility graph
• Surrogate test to distinguish between chaotic and pseudoperiodic time series
• A New Test for Chaos
• Generating surrogate data for time series with several simultaneously measured variables
• Impulses and Physiological States in Theoretical Models of Nerve Membrane

Discussions

• Max Potratzki, Manuel Adams, Timo Br\"ohl, Klaus Lehnertz: Quantifying the irregularity of a time series https://arxiv.org/abs/2512.05975 https://arxiv.org/pdf/2512.05975 https://arxiv.org/html/2512.0 [bsky, 0 points, 0 comments]

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