Recurrence plot analysis of regime changes in dynamical Systems

• Applicant: Privatdozent Dr. Norbert Marwan
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 386137731

• Final Report Year: 2021

Final Report Abstract

In summary, it can be said that this project was able to achieve the goals set, with minor exceptions. Together with our cooperating partners we were able to successfully process all working packages (WPs), except from WP3 and parts of WP2. Additionally (and as a replacement of WP3), we proposed a near-automatic approach for the proper state space reconstruction of a dynamical system, from which only a single or few measurements are available. Furthermore, we could extend this approach incorporating the research question on hand into this method. These methods substantially increase the robustness of a subsequent recurrence analysis (RA) in particular. More generally speaking, this affects all state space based techniques and we provided sound open source software packages, which could potentially lead to a big impact in dynamical systems science. We were further concerned with the impact of the most influential free parameter in RA, namely the recurrence threshold ε, and justified a way to select this threshold ensuring comparability of different recurrence plots (RPs). We have to emphasize here that this last step is essential for any running window or ensemble approach, which incorporates RPs. As for the more technical side of the RA-framework, we used the edit distance metric for obtaining RPs from irregularly sampled data and proposed border effect and line correction methods. The latter can be seen as an important step towards the general detection of dynamical transitions via line-based recurrence quantifiers. Moreover, a new RP-based quantifier – recurrence lacunarity – has been proposed and is able to detect multiscale dynamical regime transitions. On the application side, RA has successfully demonstrated its ability to classify dynamical regimes and transitions in complex systems. Specifically we were able to classify global and local (East African) climate states within the past 65 Mio. years and 620 kyrs, respectively. We further classified states and detected transitions of an instable thermoacoustic combustion process in a gas turbine. Last but not least RA was used for making statements about the change of complexity of EEG signals while executing motor-related tasks. This could be a crucial and important step for the further development of non-invasive brain control interfaces. In conclusion, this project has substantially strengthened the technical basis of RA and will, thus, help to apply this technique in even more areas, both scientifically and commercially.

Publications

• (2018). “Recurrence plot analysis of irregularly sampled data”. In: Physical Review E 98, p. 052215
  Ozken, I., D. Eroglu, S. F. M. Breitenbach, N. Marwan, L. Tan, U. Tirnakli, and J. Kurths
  
• (2018). “Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions”. In: Chaos 28.8, p. 085720
  Kraemer, K. H., R. V. Donner, J. Heitzig, and N. Marwan
  
• (2019). “Border effect corrections for diagonal line based recurrence quantification analysis measures”. In: Physics Letters A 383.34, p. 125977
  Kraemer, K. H. and N. Marwan
  
• (2019). “Classifying past climate change in the Chew Bahir basin, southern Ethiopia, using recurrence quantification analysis”. In: Climate Dynamics 53.5, pp. 2557–2572
  Trauth, M. H., A. Asrat, W. Duesing, V. Foerster, K. H. Kraemer, N. Marwan, M. A. Maslin, and F. Schaebitz
  
• (2020). “An astronomically dated record of Earth’s climate and its predictability over the last 66 million years”. In: Science 369.6509, pp. 1383–1387
  Westerhold, T., N. Marwan, A. J. Drury, D. Liebrand, et al.
  
• (2020). “Motor execution reduces EEG signals complexity: Recurrence quantification analysis study”. In: Chaos: An Interdisciplinary Journal of Nonlinear Science 30.2, p. 023111
  Pitsik, E., N. Frolov, K. Hauke Kraemer, V. Grubov, V. Maksimenko, J. Kurths, and A. Hramov
  
• (2021). “A unified and automated approach to attractor reconstruction”. In: New Journal of Physics 23, p. 033017
  Kraemer, K. H., G. Datseris, J. Kurths, I. Z. Kiss, J. L. Ocampo-Espindola, and N. Marwan
  
• (2021). “Nonlinear time series analysis of palaeoclimate proxy records”. In: Quaternary Science Reviews 274, p. 107245
  Marwan, N., J. F. Donges, R. V. Donner, and D. Eroglu
  
• “Optimal state space reconstruction via Monte Carlo Decision Tree Search”. In: Nonlinear Dynamics
  Kraemer, K. H., M. Gelbrecht, I. Pavithran, R. I. Sujith, and N. Marwan