Chaos and Time Series Analysis

Ikeguchi, Tohru; Iokibe, Tadashi; Aihara, Kazuyuki

doi:10.1007/978-4-431-67907-3_11

Cited by 9 publications

(4 citation statements)

References 38 publications

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“…Ikeguchi and Aihara [18,19] showed that the difference correlation can distinguish deterministic chaos from 1/ f α -type colored noise. The difference coefficient of correlation r 2 is the coefficient of correlation between the first-difference time series 14) where x(t i ) andx(t i ) are actual and predicted time series, x and x are the averages, and N q is the number of data points in the time series x(t i ).…”

Section: The Difference Correlationmentioning

confidence: 99%

“…Both chaos and 1/ f α -type colored noise are predictable over the short term and the conventional correlation coefficient r 1 is high. However, Ikeguchi and Aihara showed, using the difference correlation coefficient r 2 defined by (4.14), that chaos takes a high value, but 1/ f α -type colored noise takes a low value [18,19]. Figure 17 shows the conventional correlation coefficient r 1 and the difference correlation coefficient r 2 for time series data of the ship roll motion, which represent the narrow-band response of the resonant system.…”

Section: The Difference Correlationmentioning

confidence: 99%

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Quasi-chaotic behaviors of narrow-band response of a non-deterministic resonant system: application to analysis of ship motion in irregular seas

Ueno

Fan

2012

Japan J. Indust. Appl. Math.

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This paper describes similarities between the narrow-band response of a resonant system excited by random inputs and low-dimensional chaos, with particular emphasis on the geometric characteristics of trajectories reconstructed in m-dimensional phase space from measured scalar time series data with a time-delay coordinate system. In this study, the time series data of ship roll angle in irregular waves were analyzed as an example of the narrow-band response of a resonant system. These time series data were measured by one of the authors in Tokyo Bay. The similarities between the narrow-band response of a resonant system excited by random inputs and low-dimensional chaos are verified by numerical simulation data.

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Section: The Difference Correlationmentioning

confidence: 99%

Section: The Difference Correlationmentioning

confidence: 99%

Quasi-chaotic behaviors of narrow-band response of a non-deterministic resonant system: application to analysis of ship motion in irregular seas

Ueno

Fan

2012

Japan J. Indust. Appl. Math.

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“…Various problems and phenomena of importance are represented by data of time series such as weather history, stock price fluctuations, and web traffic. Thus time series analysis is an important problem in the fields of science and engineering [1,2].…”

Section: Introductionmentioning

confidence: 99%

Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equations

Terao,

Shirasaka,

Suzuki

2021

Preprint

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Nonlinear phenomena can be analyzed via linear techniques using operator-theoretic approaches. Data-driven method called the extended dynamic mode decomposition (EDMD) and its variants, which approximate the Koopman operator associated with the nonlinear phenomena, have been rapidly developing by incorporating machine learning methods. Neural ordinary differential equations (NODEs), which are a neural network equipped with a continuum of layers, and have high parameter and memory efficiencies, have been proposed. In this paper, we propose an algorithm to perform EDMD using NODEs. NODEs are used to find a parameter-efficient dictionary which provides a good finite-dimensional approximation of the Koopman operator. We show the superiority of the parameter efficiency of the proposed method through numerical experiments.

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“…The first one is based on the method of surrogate data, 4,5 which is often used in the field of chaotic time series analysis. Although the surrogate tests are effective for judging whether or not a finite sequence is produced by random, linear or nonlinear dynamics, it does not always mean that we can understand the detail of the dynamics, even if the existence of a dynamical structure is indicated by the surrogate tests.…”

Section: Introductionmentioning

confidence: 99%

Application of Chaos Game Representation to Nonlinear Time Series Analysis

2006

Self Cite

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Iterative function systems are often used for investigating fractal structures. The method is also referred as Chaos Game Representation (CGR), and is applied for representing characteristic structures of DNA sequences visually. In this paper, we proposed an original way of plotting CGR to easily confirm the property of the temporal evaluation of a time series. We also showed existence of spurious characteristic structures of time series, if we carelessly applied the CGR to real time series. We revealed that the source of spurious identification came from non-uniformity of the frequency histograms of the time series, which is often the case of analyzing real time series. We also showed how to avoid such spurious identification by applying the method of surrogate data and introducing conditional probabilities of the time series.

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Chaos and Time Series Analysis

Cited by 9 publications

References 38 publications

Quasi-chaotic behaviors of narrow-band response of a non-deterministic resonant system: application to analysis of ship motion in irregular seas

Quasi-chaotic behaviors of narrow-band response of a non-deterministic resonant system: application to analysis of ship motion in irregular seas

Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equations

Application of Chaos Game Representation to Nonlinear Time Series Analysis

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