Detecting strange attractors in turbulence

By Floris Takens. 1981

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Citations in the corpus

Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2015, background): “Fortunately, time-delay coordinates may provide useful variables from a time series (9, 12, 38).”
Loss of Chaos in Combustion Noise as a Precursor of Impending Combustion Instability (2013, background): “In such a reconstructed phase space [26], limit cycle oscillations would correspond to a closed loop around a fixed point.”
On the Implementation of the 0-1 Test for Chaos (2009, methodology): “If the equations are not known or one wishes to examine experimental data, then λ may be estimated using the phase space reconstruction method of Takens [27], by approximating the linearisation of the evolution operator [24], or by the “direct method” [23].”
Time series forecasting for nonlinear and non-stationary processes: a review and comparative study (2015, methodology): “The minimum sufficient embedding dimension m is usually estimated using a false nearest neighbor method (Takens, 1981; Kennel et al., 1992) and the optimal τ by minimizing the mutual information function (Fraser and Swinney, 1986).”
An Unsupervised Ensemble Learning Method for Nonlinear Dynamic State-Space Models (2002, background): “This is based on the theoretical result that under suitable conditions, a sequence [ x ( t ) x ( t − 1 ) . . . x ( t − D ) ] of the data vectors contains all the information needed to reconstruct the original state if the number D of the delays is large enough (Takens, 1981).”
Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. (2005, background): “Takens has proven that this equivalent attractor has the same dynamical properties (dimension, Lyapunov spectrum, entropy) as the true attractor (Takens, 1981).”
Model selection for dynamical systems via sparse regression and information criteria (2017, background): “of the system without measurements from all the ‘natural’ state variables [39].”
Recurrence networks—a novel paradigm for nonlinear time series analysis (2009, methodology): “, N), one may use a suitable m-dimensional time delay embedding of x(t) with delay τ [11], x(t) = (x(t), x(t+ τ), .”
A Non-Parametric Independence Test Using Permutation Entropy (2008, methodology): “The process of symbolizing a time series is based upon the method of delay time coordinates, introduced by Takens (1981), in order to carry out the phase space reconstruction.”