Trends in recurrence analysis of dynamical systems

Abstract

The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot-based data analysis and to widen its application potential. We will give a brief overview about important and innovative developments, such as computational improvements, alternative recurrence definitions (event-like, multiscale, heterogeneous, and spatio-temporal recurrences) and ideas for parameter selection, theoretical considerations of recurrence quantification measures, new recurrence quantifiers (e.g. for transition detection and causality detection), and correction schemes. New perspectives have recently been opened by combining recurrence plots with machine learning. We finally show open questions and perspectives for futures directions of methodical research.

Classification of Motor-Imagery Tasks Using a Large EEG Dataset by Fusing Classifiers Learning on Wavelet-Scattering Features

“…However, the estimations of these two parameters using FNN and AMI for the phase-space reconstruction of each EEG signal are deemed not effective for feature extraction because the signals may result in features with different dimensions. This issue still remains open for research in recurrence analysis [37], and it has been reported that optimal selections of values for m are problem-dependent [38]. Having discussed in [39], the FCM, which is adopted for constructing an FRP, is governed by two input parameters c and β.…”

Challenges and perspectives in recurrence analyses of event time series

“…Another class of methods are based on the property of recurrences of states. In general, recurrence based methods provide versatile approaches for classifying data, identification of regime transitions, but also for unveiling interrelationships, synchronization, and causal links between different dynamical systems [20][21][22][23]. Due to its broad usability, simplicity, and growing number of software allowing recurrence analysis [24], this method is attracting more and more interest and becoming increasingly popular [23,25].…”

Critical recurrence scale thresholds

“…Recurrence quantification analysis (RQA) [1] is a computational approach of increasing popularity [2], which is used for deducing a wide range of signatures that, in some sense, characterize dynamical processes. Often, the resulting RQA indices can be linked to structural stability properties, for instance, by establishing relations to dynamical entropies or Lyapunov exponents.…”