Journal ArticleDOI
Reconstruction expansion as a geometry-based framework for choosing proper delay times
TLDR
In this article, the authors developed a new, computationally efficient approach to choosing τ that quantifies reconstruction expansion from the identity line of the embedding space, and showed that reconstruction expansion is related to the concept of reconstruction signal strength and that increased expansion corresponds to diminished effects of measurement error.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1994-05-15. It has received 387 citations till now. The article focuses on the topics: Attractor.read more
Citations
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Journal ArticleDOI
Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field
TL;DR: Interpretation of results in terms of 'functional sources' and 'functional networks' allows the identification of three basic patterns of brain dynamics: normal, ongoing dynamics during a no-task, resting state in healthy subjects, and hypersynchronous, highly nonlinear dynamics of epileptic seizures and degenerative encephalopathies.
Journal ArticleDOI
Nonlinear dynamics, delay times, and embedding windows
TL;DR: In this article, the authors proposed a simpler method for estimating the delay time of a nonlinear time series using the correlation integral, which is known as the C-C method.
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Chaos in Chen's system with a fractional order
Changpin Li,Guojun Peng +1 more
TL;DR: In this paper, the authors used fractional calculus techniques to construct phase diagrams in Chen's system with fractional order and found that chaos does exist in the system with a fractional ordering, and some phase diagrams are constructed.
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The influence of gait speed on local dynamic stability of walking
TL;DR: A monotonic trend between lambda(Max) and walking velocity was observed and suggests that slower walking velocities lead to increases in stability, which may reveal more detailed information on the behavior of the neuro-controller than variability-based analyses alone.
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Epileptic seizures can be anticipated by non-linear analysis
Jacques Martinerie,Claude Adam,M. Le Van Quyen,Michel Baulac,S. Clemenceau,Bernard Renault,Francisco J. Varela +6 more
TL;DR: It is demonstrated that in most cases, seizure onset could be anticipated well in advance (between 2–6 minutes beforehand), and that all subjects seemed to share a similar 'route' towards seizure.
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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Characterization of Strange Attractors
TL;DR: In this article, a measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable, and the relation of this measure to fractal dimension and information-theoretic entropy is discussed.
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Independent coordinates for strange attractors from mutual information.
TL;DR: In this paper, the mutual information I is examined for a model dynamical system and for chaotic data from an experiment on the Belousov-Zhabotinskii reaction.
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Oscillation and Chaos in Physiological Control Systems
Michael C. Mackey,Leon Glass +1 more
TL;DR: First-order nonlinear differential-delay equations describing physiological control systems displaying a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions are studied.