Trends in recurrence analysis of dynamical systems

TL;DR

This paper reviews recent advances in recurrence analysis of dynamical systems, highlighting computational, theoretical, and application developments, and discusses future research directions including machine learning integration.

Contribution

It provides a comprehensive overview of innovative developments in recurrence analysis, including new definitions, quantifiers, and integration with machine learning.

Findings

Introduction of alternative recurrence definitions

Development of new recurrence quantifiers

Discussion of future research directions

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.