Trends in recurrence analysis of dynamical systems

@article{Marwan2023TrendsIR,
  title={Trends in recurrence analysis of dynamical systems},
  author={Norbert Marwan and K. Hauke Kraemer and Standalone App},
  journal={The European Physical Journal Special Topics},
  year={2023},
  volume={232},
  pages={5-27},
  url={https://api.semanticscholar.org/CorpusID:255630484}
}
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, and open questions and perspectives for futures directions of methodical research are shown.
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44 Citations
Background Citations
7
Methods Citations
4

44 Citations

Special Issue “Trends in recurrence analysis of dynamical systems”

An attempt to provide an overview of the most significant technical developments of this recurrence-plot-based framework in the past decade is included in this special issue.

An algorithm for simplified recurrence analysis.

Recurrence analysis applications are hindered by several issues including the selection of critical parameters, noise sensitivity, computational complexity, or the analysis of non-stationary systems.…

Density-based recurrence measures from microstates.

This approach opens up a line of research by reframing traditional RQAs in terms of microstates, and establishes a bridge between concepts of traditional lines-based RQA and recurrence microstates.

Classifying Complex Dynamical and Stochastic Systems via Physics-Based Recurrence Features

This study employs the recently developed recurrence microstate probabilities as features to improve accuracy of several well-established machine learning (ML) algorithms, and demonstrates that a few optimal machine learning algorithms are particularly effective for classification when combined with recurrence microstates.

Interpolation and sampling effects on recurrence quantification measures.

The recurrence plot and the recurrence quantification analysis (RQA) are well-established methods for the analysis of data from complex systems. They provide important insights into the nature of the…

Challenges and perspectives in recurrence analyses of event time series

Recurrence analysis, a powerful concept from nonlinear time series analysis, provides several opportunities to work with event data and even for the most challenging task of comparing event time series with continuous time series.

Energy-efficient recurrence quantification analysis

Strategies to compute RQA measures directly from time series or phase space vectors, avoiding the need to construct RPs are introduced, contributing to energy saving and sustainable data analysis, and broaden the applicability of recurrence-based methods in modern research contexts.

Exploring recursive properties and dynamical complexity in scalar time-series using threshold-free recursive analysis approach

In this project, a threshold-free recursive analysis approach was investigated to reveal the recursive properties of dynamic systems. Specifically, the occurrence of recurrent patterns in phase…

Machine learning approach to detect dynamical states from recurrence measures

This study integrates machine learning approaches with nonlinear time series analysis, specifically utilizing recurrence measures to classify various dynamical states emerging from time series, and illustrates how the trained algorithms can successfully predict the dynamical states of two variable stars.

Multivariate data analysis using recurrence measures

The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different…

181 References

Recurrence plots 25 years later —Gaining confidence in dynamical transitions

Recurrence-plot–based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies…

Finding recurrence networks' threshold adaptively for a specific time series

A comparison between the constant threshold and adaptive threshold cases is shown to study period–chaos and even period–period transitions in the dynamics of a prototypical model system.

Optimal estimation of recurrence structures from time series

A stochastic Markov model for the recurrent dynamics that allows for the analytical derivation of a criterion for the optimal distance threshold and the number of optimal recurrence domains as a statistic for classifying an animals' state of consciousness is proposed.

A Refinement of Recurrence Analysis to Determine the Time Delay of Causality in Presence of External Perturbations

A refinement of recurrence analysis to determine the delay in the causal influence between a driver and a target, in the presence of additional perturbations affecting the time series of the response observable.

Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure

Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots and contributes to a better distinction between stable operation and near blowout states of combustors.

Recurrence-based time series analysis by means of complex network methods

Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and substantially enrich the knowledge gathered from other existing approaches.

How to Avoid Potential Pitfalls in Recurrence Plot Based Data Analysis

Potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis are pointed out.

Recurrence plots revisited

Geometric detection of coupling directions by means of inter-system recurrence networks

Analytical framework for recurrence network analysis of time series.

Theoretical framework for a number of archetypical chaotic attractors such as those of the Bernoulli and logistic maps, periodic and two-dimensional quasiperiodic motions, and for hyperballs and hypercubes are illustrated.
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