Compressing Phase Space Detects State Changes in Nonlinear Dynamical Systems
Equations governing the nonlinear dynamics of complex systems are usually unknown, and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences to be accurate. In this paper, we show that an optimal rec...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/8650742 |
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| _version_ | 1849399644177563648 |
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| author | Valeria d’Andrea Manlio De Domenico |
| author_facet | Valeria d’Andrea Manlio De Domenico |
| author_sort | Valeria d’Andrea |
| collection | DOAJ |
| description | Equations governing the nonlinear dynamics of complex systems are usually unknown, and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences to be accurate. In this paper, we show that an optimal reconstruction can be achieved by lossless compression of system’s time course, providing a self-consistent analysis of its dynamics and a measure of its complexity, even for short sequences. Our measure of complexity detects system’s state changes such as weak synchronization phenomena, characterizing many systems, in one step, integrating results from Lyapunov and fractal analysis. |
| format | Article |
| id | doaj-art-9d1e69d8fd1f4c0f8a22635f30030fbc |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-9d1e69d8fd1f4c0f8a22635f30030fbc2025-08-20T03:38:16ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/86507428650742Compressing Phase Space Detects State Changes in Nonlinear Dynamical SystemsValeria d’Andrea0Manlio De Domenico1CoMuNe Lab, Fondazione Bruno Kessler, Via Sommarive 18, Povo, Trento 38123, ItalyCoMuNe Lab, Fondazione Bruno Kessler, Via Sommarive 18, Povo, Trento 38123, ItalyEquations governing the nonlinear dynamics of complex systems are usually unknown, and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences to be accurate. In this paper, we show that an optimal reconstruction can be achieved by lossless compression of system’s time course, providing a self-consistent analysis of its dynamics and a measure of its complexity, even for short sequences. Our measure of complexity detects system’s state changes such as weak synchronization phenomena, characterizing many systems, in one step, integrating results from Lyapunov and fractal analysis.http://dx.doi.org/10.1155/2020/8650742 |
| spellingShingle | Valeria d’Andrea Manlio De Domenico Compressing Phase Space Detects State Changes in Nonlinear Dynamical Systems Complexity |
| title | Compressing Phase Space Detects State Changes in Nonlinear Dynamical Systems |
| title_full | Compressing Phase Space Detects State Changes in Nonlinear Dynamical Systems |
| title_fullStr | Compressing Phase Space Detects State Changes in Nonlinear Dynamical Systems |
| title_full_unstemmed | Compressing Phase Space Detects State Changes in Nonlinear Dynamical Systems |
| title_short | Compressing Phase Space Detects State Changes in Nonlinear Dynamical Systems |
| title_sort | compressing phase space detects state changes in nonlinear dynamical systems |
| url | http://dx.doi.org/10.1155/2020/8650742 |
| work_keys_str_mv | AT valeriadandrea compressingphasespacedetectsstatechangesinnonlineardynamicalsystems AT manliodedomenico compressingphasespacedetectsstatechangesinnonlineardynamicalsystems |