Quantifying the irregularity of a time series
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914229553987584 |
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| author | Potratzki, Max Adams, Manuel Bröhl, Timo Lehnertz, Klaus |
| author_facet | Potratzki, Max Adams, Manuel Bröhl, Timo Lehnertz, Klaus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05975 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantifying the irregularity of a time series Potratzki, Max Adams, Manuel Bröhl, Timo Lehnertz, Klaus Chaotic Dynamics Data Analysis, Statistics and Probability 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. |
| title | Quantifying the irregularity of a time series |
| topic | Chaotic Dynamics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2512.05975 |