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Front. Appl. Math. Stat., 14 August 2020 |

Editorial: Recurrence Analysis of Complex Systems Dynamics

  • 1Bernstein Center for Computational Neuroscience, Berlin, Germany
  • 2Team MIMESIS, INRIA Nancy – Grand Est, Strasbourg, France
  • 3Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, Complexity Science, Potsdam, Germany
  • 4Institute of Geoscience, University of Potsdam, Potsdam, Germany
  • 5Faculty of Engineering, Ansbach University of Applied Sciences, Ansbach, Germany
  • 6Stritch School of Medicine, Loyola University Chicago, Chicago, IL, United States

Editorial on the Research Topic
Recurrence Analysis of Complex Systems Dynamics

In the last three decades, recurrence plot (RP) and quantification (RQA) techniques have become important research tools in the analysis of short, noisy, and non-stationary data. Theoretical work on RPs has reached considerable maturity, and the method's popularity in recent years continues to increase due to a large number of practical RP/RQA applications in diverse areas such as physiology, human cognition, engineering, or earth and climate sciences.

This Frontiers Research Topic presents novel advances and new applications of recurrence methods for analyzing complex systems in multidisciplinary fields. For instance, such complex systems may represent spatial systems, whose spatiotemporal dynamics may exhibit recurrences in localized regions only. To analyze the recurrent structure in such local areas, Bonizzi et al. show how the critical regions can first be identified prior to analyzing the local recurrent structures therein. Application to experimental cardiac heart rate data demonstrates the power of the method.

To better understand complex systems and the origin of recurrences, it is important to understand the coupling between sub-units in complex systems. Tolston et al. focus their work on detecting the coupling strength in nonlinear systems. To this end, they compare the nonlinear recurrence analysis with linear cross-correlation analysis and evaluate them using simulated data and experimental interpersonal dynamics data. The authors show that cross-correlation analysis may perform comparably well as recurrence analysis methods, while the linear method is computationally more efficient.

Typically, recurrence analysis is applied to digitized sampled data obtained from an analog complex system. Conversely, Hasselmann and Bosman analyze self-reports of human experience, that are written consecutively over a long series of days. The authors discuss formal, practical, and theoretical issues of such data and introduce the concept of recurrence networks weighted by recurrence time. They conclude that their complex systems approach to analyzing self-reports of human experience is preferable over conventional statistical analysis.

This latter study shows that recurrence analysis is able to extract knowledge from non-standard data sets, e.g., by quantifying cognitive behavior. As an additional example, Angus reviews recurrence analysis techniques applied to human communication data. He concludes that recurrence analysis is a promising tool to analyze human discourse data. Moreover, cognitive behavior is revealed in written text as shown by Lyby et al. The authors detect changes in distress symptoms in cancer patients by recurrence analysis, which points to the patients' cognitive restructuring.

In medicine, recurrence analysis provides some deeper insights into the underlying physiological dynamics during cognitive requests. For instance, the heart-rate regulatory system is known to form a complex network, which exhibits recurrent dynamics. Dimitriev et al. have studied the heart rate recurrences during mental stress and identified mental workload by recurrence variables.

Even in resting state, i.e., in the absence of cognitive tasks, physiological data exhibit recurrent structures. beim Graben et al. have identified a large number of recurrent metastable states in fMRI-data by recurrence analysis. These states are approached, maintained, and exited subsequently in the course of time, which demonstrates that the brain is active although no cognitive task is present.

Besides cognitive and physiological dynamics in humans, other natural complex systems exhibit recurrent structures as well. Salas et al. reveal the relationship between El Niño-Southern Oscillation and monthly hydrological anomalies of rainfall and stream flows in Colombia by recurrence analysis techniques. The authors show that the hydrological dynamics of Colombia exhibits generalized synchronization with the El Niño-Southern Oscillations.

Author Contributions

AH has conceived the structure of the Editorial and all authors have written the Editorial.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Keywords: recurrence analysis, medicine, psychology, meteorology, neuroscience

Citation: beim Graben P, Hutt A, Marwan N, Uhl C and Webber CL Jr (2020) Editorial: Recurrence Analysis of Complex Systems Dynamics. Front. Appl. Math. Stat. 6:33. doi: 10.3389/fams.2020.00033

Received: 26 June 2020; Accepted: 10 July 2020;
Published: 14 August 2020.

Approved by:

Isao T. Tokuda, Ritsumeikan University, Japan

Copyright © 2020 beim Graben, Hutt, Marwan, Uhl and Webber. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Axel Hutt,