Journal ArticleDOI
Recurrence Plots of Dynamical Systems
TLDR
In this article, a graphical tool for measuring the time constancy of dynamical systems is presented and illustrated with typical examples, and the tool can be used to measure the time complexity of a dynamical system.Abstract:
A new graphical tool for measuring the time constancy of dynamical systems is presented and illustrated with typical examples.read more
Citations
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Journal ArticleDOI
Recurrence plots for the analysis of complex systems
TL;DR: The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research, and detail the analysis of data and indicate possible difficulties and pitfalls.
Journal ArticleDOI
Heart rate variability: a review
TL;DR: The various applications of HRV and different linear, frequency domain, wavelet domain, nonlinear techniques used for the analysis of the HRV are discussed.
Journal ArticleDOI
Practical implementation of nonlinear time series methods: The TISEAN package.
TL;DR: In this paper, the authors describe the implementation of methods of nonlinear time series analysis which are based on the paradigm of deterministic chaos and present a variety of algorithms for data representation, prediction, noise reduction, dimension and Lyapunov estimation.
Journal ArticleDOI
Practical implementation of nonlinear time series methods: The TISEAN package
TL;DR: A variety of algorithms for data representation, prediction, noise reduction, dimension and Lyapunov estimation, and nonlinearity testing are discussed with particular emphasis on issues of implementation and choice of parameters.
Journal ArticleDOI
Dynamical assessment of physiological systems and states using recurrence plot strategies
TL;DR: This paper illustrates how recurrence plots can take single physiological measurements, project them into multidimensional space by embedding procedures, and identify time correlations (recurrences) that are not apparent in the one-dimensional time series.
References
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Journal ArticleDOI
Ergodic theory of chaos and strange attractors
Jean-Pierre Eckmann,David Ruelle +1 more
TL;DR: A review of the main mathematical ideas and their concrete implementation in analyzing experiments can be found in this paper, where the main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions).
Journal ArticleDOI
Liapunov exponents from time series.
TL;DR: An algorithm for computing Liapunov exponents from an experimental time series is analyzed and a hydrodynamic experiment is investigated.
Journal ArticleDOI
Roads to turbulence in dissipative dynamical systems
TL;DR: In this article, three scenarios leading to turbulence in theory and experiment are outlined, and the respective mathematical theories are explained and compared, and three different models of turbulence are discussed. But none of the scenarios are discussed in detail.
Journal ArticleDOI
Diagnosis of dynamical systems with fluctuating parameters
TL;DR: In this article, it is argued that many time evolutions occurring in Nature may be considered as non-autonomous, but dependent on parameters that vary slowly with time, and that some, but not all, of the tools used to understand chaotic dynamics remain useful in this situation.