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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2407.13452 |
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| _version_ | 1866929426506186752 |
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| author | Sándor, Bulcsú Rusu, András Dénes, Károly Ercsey-Ravasz, Mária Lázár, Zsolt I. |
| author_facet | Sándor, Bulcsú Rusu, András Dénes, Károly Ercsey-Ravasz, Mária Lázár, Zsolt I. |
| contents | There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the underlying chaotic systems is a notoriously difficult task. Building on prior theoretical studies that focus on the discontinuities at $q=1$ in the order-$q$ Rényi-entropy of the trajectory space, we measure the derivative of the spectrum. We derive within the general context of Markov processes a computationally efficient closed-form expression for this measure. We investigate its properties through well-known dynamical systems exploring its scope and limitations. The proposed mathematical instrument can serve as a predictor of dynamical phase transitions in time series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13452 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Measuring dynamical phase transitions in time series Sándor, Bulcsú Rusu, András Dénes, Károly Ercsey-Ravasz, Mária Lázár, Zsolt I. Chaotic Dynamics Data Analysis, Statistics and Probability 37N99 There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the underlying chaotic systems is a notoriously difficult task. Building on prior theoretical studies that focus on the discontinuities at $q=1$ in the order-$q$ Rényi-entropy of the trajectory space, we measure the derivative of the spectrum. We derive within the general context of Markov processes a computationally efficient closed-form expression for this measure. We investigate its properties through well-known dynamical systems exploring its scope and limitations. The proposed mathematical instrument can serve as a predictor of dynamical phase transitions in time series. |
| title | Measuring dynamical phase transitions in time series |
| topic | Chaotic Dynamics Data Analysis, Statistics and Probability 37N99 |
| url | https://arxiv.org/abs/2407.13452 |