Journal ArticleDOI
Measuring the Strangeness of Strange Attractors
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TLDR
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.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1983-10-01. It has received 5239 citations till now. The article focuses on the topics: Correlation dimension & Lyapunov exponent.read more
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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).
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Determining embedding dimension for phase-space reconstruction using a geometrical construction
TL;DR: The issue of determining an acceptable minimum embedding dimension is examined by looking at the behavior of near neighbors under changes in the embedding dimensions from d\ensuremath{\rightarrow}d+1 by examining the manner in which noise changes the determination of ${\mathit{d}}_{\math it{E}}$.
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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.
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A test for independence based on the correlation dimension
TL;DR: In this paper, the authors present a test of independence that can be applied to the estimated residuals of any time series model, which can be transformed into a model driven by independent and identically distributed errors.
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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.
References
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Journal ArticleDOI
Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
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An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
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An Introduction to Probability Theory and Its Applications.
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Simple mathematical models with very complicated dynamics
Robert M. May,Robert M. May +1 more
TL;DR: This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.