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.

arXiv comment34 pages, 14 figures, 1 table

References in corpus (30)

• Recurrence Plots for the Analysis of Complex Systems
• Surrogate time series
• Complex network approaches to nonlinear time series analysis
• Recurrence networks - A novel paradigm for nonlinear time series analysis
• Recurrence-based time series analysis by means of complex network methods
• Nonlinear time-series analysis revisited
• How to avoid potential pitfalls in recurrence plot based data analysis
• Recurrence plot statistics and the effect of embedding
• Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package
• Analytical framework for recurrence-network analysis of time series
• Generalised Recurrence Plot Analysis for Spatial Data
• Geometric detection of coupling directions by means of inter-system recurrence networks
• Recurrence Plots 25 years later -- gaining confidence in dynamical transitions
• Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions
• Forecasting with time series imaging
• PyRQA -- Conducting Recurrence Quantification Analysis on Very Long Time Series Efficiently
• Detecting recurrence domains of dynamical systems by symbolic dynamics
• A unified and automated approach to attractor reconstruction
• Optimal reconstruction of dynamical systems: A noise amplification approach
• Kolmogorov-Sinai entropy from recurrence times
• Prediction in Projection
• Optimal Estimation of Recurrence Structures from Time Series
• Strong laws for recurrence quantification analysis
• Optimal Markov Approximations and Generalized Embeddings
• Radius selection using kernel density estimation for the computation of nonlinear measures
• Averaged Recurrence Quantification Analysis -- Method omitting the recurrence threshold choice
• Recurrence Network Analysis of Exoplanetary Observables
• Transformation cost spectrum for irregularly sampled time series
• Extended generalized recurrence plot quantification of complex circular patterns
• Visualizing driving forces of spatially extended systems using the recurrence plot framework

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