Analysis of observed chaotic data

By Mehmet Emre Cek. 2004

1,122 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/84a07bccf7e39223dc6797336466cd7c43b0ec49

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Citations in the corpus

Comparison of systems with complex behavior (2004, methodology): “This observation lead to the development of the Takens embedding theorem [38], that was followed by a large number of works in which the theorem was used to illuminate topological properties of experimental data sets [1].”
EC-SVM approach for real-time hydrologic forecasting (2004, methodology): “Abarbanel (1996) proposed that the time delay t should be chosen when AMI occurs at its first minimum. With this t value, the embedding dimension d is selected associated with the minimum false nearest neighbours. The prediction is then based on such embedding and utilises a local model through the ”
Statistical inference for dynamical systems: A review (2012, background): “Furthermore, let us mention the following books or monographs related to the topics in this survey: [1, 8, 14, 29, 62, 64, 91, 118].”
Is correlation dimension a reliable indicator of low‐dimensional chaos in short hydrological time series? (2002, unknown): “The local map FT, which does this, is determined by a least squares fit minimizing Xk p¼1 Y p jþ1 FTY p j 2 : ð3Þ In this study, the local maps are learned in the form of local polynomials [e.g., Abarbanel, 1996], and the predictions are made forward from a new point Z0 using these local maps.”
The dynamics of human gait (2005, background): “While there exist excellent monographs on nonlinear time series analysis [4–6], there is still a shortage of literature showing concrete applications of simple methods to real-life problems.”
Smooth estimation of a distribution and density function on a hypercube using Bernstein polynomials for dependent random vectors (2006, methodology): “Under the assumption that τ admits an absolutely continuous invariant measure given by the density fτ , it is useful to estimate fτ and τ ′, the derivative of τ to obtain a plug-in estimator of metric entropy h(τ) (see Abarbanel (1995)) given by”
EEG Signal Analysis: A Survey (2010, methodology): “To obtain a recurrence plot from time series, the embedding dimension (m) is chosen by method of delays [1].”
Analysis of cycle-to-cycle pressure oscillations in a diesel engine (2008, methodology): “For an MIP time series, the AMI is given by the expression [1,31]:”
Data-driven modelling: some past experiences and new approaches (2008, background): “Chaos theory and nonlinear dynamics appear to be useful for time series forecasting when a time series carries enough information about the behaviour of the system (Abarbanel 1996). Let a time series {x1, x2, ... , xt, ... , xn } be given (e.g. a sequence of water levels). The state of the system at”
Stochastic simulation model for nonstationary time series using an autoregressive wavelet decomposition: Applications to rainfall and temperature (2007, background): “The idea of decomposing the time series into components that correspond to simpler dynamical systems with characteristic dynamics at particular scales is pragmatically attractive, even though a low-order nonlinear autoregressive model [e.g., Abarbanel, 1996; Abarbanel and Lall, 1996] that automati”
Nonlinear self-excited thermoacoustic oscillations: intermittency and flame blowout (2012, background): “A detailed discussion of the various algorithms for choosing the optimum time delay and embedding dimension can be found in Abarbanel (1996) and Kantz & Schreiber (2003).”
Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics (2019, methodology): “The Lyapunov spectrum of the Lorenz96 system is calculated using a standard technique based on QR decomposition (Abarbanel, 2012).”
Predicting monthly streamflow using data‐driven models coupled with data‐preprocessing techniques (2009, methodology): “The FNN algorithm was originally developed for determining the number of time-delay coordinates needed to recreate autonomous dynamics directly from properties of the data themselves [Kennel et al., 1992; Abarbanel et al., 1993].”
Nonlinear Dynamical System Identification from Uncertain and Indirect Measurements (2004, unknown): “…dimension for noisy data than a precise estimation of correlation dimensions [Grassberger & Procaccia, 1983a, 1983b; Grassberger et al., 1991; Albano et al., 1988] is based on the false nearest-neighbor approach [Kennel et al., 1992; Abarbanel et al., 1993; Abarbanel, 1996; Hegger & Kantz, 1999].”
Neural networks and M5 model trees in modelling water level-discharge relationship (2005, methodology): “For discrete measurements the actual AMI-values depend on the number of class intervals used to calculate the probability densities [1].”