An Investigation into the Use of Delay Coordinate Embedding Technique with MIMO ANFIS for Nonlinear Prediction of Chaotic Signals

2005 ◽  
pp. 677-688
Author(s):  
Jun Zhang ◽  
Weiwei Dai ◽  
Muhui Fan ◽  
Henry Chung ◽  
Zhi Wei ◽  
...  
Keyword(s):  
Nonlinear Prediction ◽  
Embedding Technique ◽  
Chaotic Signals ◽  
Delay Coordinate Embedding ◽  
Coordinate Embedding

Experimental Evidence of Quasiperiodicity and Its Breakdown in the Column-Pendulum Oscillator

1995 ◽  
Vol 117 (2) ◽  
pp. 218-225 ◽  
Author(s):  
G. Mustafa ◽  
A. Ertas
Keyword(s):  
Fourier Spectrum ◽  
Invariant Tori ◽  
Flexible Structures ◽  
Experimental System ◽  
Experimental Dynamics ◽  
Resonance Overlap ◽  
Embedding Technique ◽  
Onset Of Turbulence ◽  
Delay Coordinate Embedding ◽  
Coordinate Embedding

A new vibration absorbing device is introduced for large flexible structures. The phase-space of the experimental system is reconstructed via delay-coordinate embedding technique. Experimental dynamics indicate that the motion is predominantly quasiperiodic, confirming the existence of invariant tori. Within the quasi-periodic region, there are windows containing intricate webs of phase-locked periodic responses. The quasiperiodic and the phase-locked responses are clearly visualized on the cover of the torus. Increase in the amplitude of excitation results in distortion of the invariant torus due to the resonance overlap. Due to the resonance overlap, the return map extracted from the experimental data becomes noninvertible. Furthermore, a burst of frequencies appears on the Fourier spectrum. This scenario is similar to many experimental observations of hydrodynamical instabilities; the breakup of the tori in these experiments is related to the onset of turbulence.

EXPERIMENTAL CONTROL OF CHAOS BY MODIFICATIONS OF DELAYED FEEDBACK

2001 ◽  
Vol 11 (12) ◽  
pp. 3125-3132 ◽  
Author(s):  
KAZUYUKI YAGASAKI ◽  
YOSHIYUKI TOCHIO
Keyword(s):  
Experimental System ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Control Technique ◽  
Control Force ◽  
Unstable Periodic Orbits ◽  
System A ◽  
Embedding Technique ◽  
Delay Coordinate Embedding ◽  
Coordinate Embedding

We present two modifications of the delayed feedback control technique for controlling chaotic dynamical systems. In these methods, control force is applied only when trajectories enter neighborhoods of the targets. So three shortcomings in the delayed feedback technique, the nonsmallness of control force, impossibility of targeting unstable periodic orbits and birth of undesirable stable orbits, are improved. The delay coordinate embedding technique is also used for specifying the target orbits and determining whether trajectories enter their neighborhood. We demonstrate the effectiveness of the two approaches for an experimental system, a feedback controlled pendulum.

scholarly journals Estimating Conditional Transfer Entropy in Time Series Using Mutual Information and Nonlinear Prediction

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1124
Author(s):  
Payam Shahsavari Baboukani ◽  
Carina Graversen ◽  
Emina Alickovic ◽  
Jan Østergaard
Keyword(s):  
Time Series ◽  
State Of The Art ◽  
Difficult Case ◽  
Nonlinear Prediction ◽  
False Detection ◽  
Uniform Embedding ◽  
Embedding Technique ◽  
New Information ◽  
Highly Correlated ◽  
Intracranial Electroencephalography

We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of new information and improvement of the prediction accuracy provided by the variables. Then, using a greedy approach, the most informative subsets are selected in an iterative way. The algorithm terminates, when the highest ranked variable is not able to significantly improve the accuracy of the prediction as compared to that obtained using the existing selected subsets. In a simulation study, we compare our estimator to existing state-of-the-art methods at different data lengths and directed dependencies strengths. It is demonstrated that the proposed estimator has a significantly higher accuracy than that of existing methods, especially for the difficult case, where the data are highly correlated and coupled. Moreover, we show its false detection of directed dependencies due to instantaneous couplings effect is lower than that of existing measures. We also show applicability of the proposed estimator on real intracranial electroencephalography data.

Explicit Realization of Chaos Control in an NMR-Laser Experiment

1993 ◽  
Vol 48 (5-6) ◽  
pp. 627-628
Author(s):  
J. Parisi ◽  
R. Badii ◽  
E. Brun ◽  
L. Flepp ◽  
C. Reyl ◽  
...  
Keyword(s):  
Control Method ◽  
Laser System ◽  
Small Time ◽  
System Quality ◽  
Real Time Control ◽  
Time Control ◽  
Explicit Realization ◽  
Delay Coordinate Embedding ◽  
The Stability ◽  
Coordinate Embedding

Abstract The usefulness of the Ott-Grebogi-Yorke control method is demonstrated by stabilizing a chaotic NMR-laser system around an unstable period-one orbit. We have used a six-dimensional delay-coordinate embedding technique in order to fully determine the stability properties of the orbit controlled. Our analysis yields small time-dependent perturbations of the system quality factor capable to perform real-time control.

Recent Developments in Chaotic Time Series Analysis

2003 ◽  
Vol 13 (06) ◽  
pp. 1383-1422 ◽  
Author(s):  
Ying-Cheng Lai ◽  
Nong Ye
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Hilbert Transform ◽  
Chaotic Time Series ◽  
Unstable Periodic Orbits ◽  
Series Analysis ◽  
Delay Coordinate Embedding ◽  
The Hilbert Transform ◽  
Chaotic Time Series Analysis ◽  
Coordinate Embedding

In this paper, two issues are addressed: (1) the applicability of the delay-coordinate embedding method to transient chaotic time series analysis, and (2) the Hilbert transform methodology for chaotic signal processing.A common practice in chaotic time series analysis has been to reconstruct the phase space by utilizing the delay-coordinate embedding technique, and then to compute dynamical invariant quantities of interest such as unstable periodic orbits, the fractal dimension of the underlying chaotic set, and its Lyapunov spectrum. As a large body of literature exists on applying the technique to time series from chaotic attractors, a relatively unexplored issue is its applicability to dynamical systems that exhibit transient chaos. Our focus will be on the analysis of transient chaotic time series. We will argue and provide numerical support that the current delay-coordinate embedding techniques for extracting unstable periodic orbits, for estimating the fractal dimension, and for computing the Lyapunov exponents can be readily adapted to transient chaotic time series.A technique that is gaining an increasing attention is the Hilbert transform method for signal processing in nonlinear systems. The general goal of the Hilbert method is to assess the spectrum of the instantaneous frequency associated with the underlying dynamical process. To obtain physically meaningful results, it is necessary for the signal to possess a proper rotational structure in the complex plane of the analytic signal constructed by the original signal and its Hilbert transform. We will describe a recent decomposition procedure for this task and apply the technique to chaotic signals. We will also provide an example to demonstrate that the methodology can be useful for addressing some fundamental problems in chaotic dynamics.

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