Journal ArticleDOI
Dynamical assessment of physiological systems and states using recurrence plot strategies
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TLDR
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.Abstract:
Physiological systems are best characterized as complex dynamical processes that are continuously subjected to and updated by nonlinear feedforward and feedback inputs. System outputs usually exhibit wide varieties of behaviors due to dynamical interactions between system components, external noise perturbations, and physiological state changes. Complicated interactions occur at a variety of hierarchial levels and involve a number of interacting variables, many of which are unavailable for experimental measurement. In this paper we illustrate 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. We extend the original description of recurrence plots by computing an array of specific recurrence variables that quantify the deterministic structure and complexity of the plot. We then demonstrate how physiological states can be assessed by making repeated recurrence plot calculations within a window sliding down any physiological dynamic. Unlike other predominant time series techniques, recurrence plot analyses are not limited by data stationarity and size constraints. Pertinent physiological examples from respiratory and skeletal motor systems illustrate the utility of recurrence plots in the diagnosis of nonlinear systems. The methodology is fully applicable to any rhythmical system, whether it be mechanical, electrical, neural, hormonal, chemical, or even spacial.read more
Citations
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References
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Journal ArticleDOI
Measuring the Strangeness of Strange Attractors
TL;DR: In this paper, the correlation exponent v is introduced as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise, and algorithms for extracting v from the time series of a single variable are proposed.
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Recurrence Plots of Dynamical Systems
TL;DR: 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.
Journal ArticleDOI
Embeddings and delays as derived from quantification of recurrence plots
TL;DR: Recurrence plots have been advocated as a useful diagnostic tool for the assessment of dynamical time series by quantifying certain features of these plots which may be helpful in determining embeddings and delays.
Journal ArticleDOI
Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems
Jean-Pierre Eckmann,David Ruelle +1 more
TL;DR: In this paper, it was shown that the correlation dimension of the Grassberger-Procaccia algorithm cannot exceed the value 2 log 10N if N is the number of points in the time series, and when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present.