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Titlebook: Nonlinear Dynamics and Statistics; Alistair I. Mees Book 2001 Springer Science+Business Media New York 2001 Monte Carlo method.Time series

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发表于 2025-3-21 20:00:15 | 显示全部楼层 |阅读模式
书目名称Nonlinear Dynamics and Statistics
编辑Alistair I. Mees
视频video
图书封面Titlebook: Nonlinear Dynamics and Statistics;  Alistair I. Mees Book 2001 Springer Science+Business Media New York 2001 Monte Carlo method.Time series
描述All models are lies. "The Earth orbits the sun in an ellipse with the sun at one focus" is false, but accurate enough for almost all purposes. This book describes the current state of the art of telling useful lies about time-varying systems in the real world. Specifically, it is about trying to "understand" (that is, tell useful lies about) dynamical systems directly from observa­ tions, either because they are too complex to model in the conventional way or because they are simply ill-understood. B(:cause it overlaps with conventional time-series analysis, building mod­ els of nonlinear dynamical systems directly from data has been seen by some observers as a somewhat ill-informed attempt to reinvent time-series analysis. The truth is distinctly less trivial. It is surely impossible, except in a few special cases, to re-create Newton‘s astonishing feat of writing a short equation that is an excellent description of real-world phenomena. Real systems are connected to the rest of the world; they are noisy, non­ stationary, and have high-dimensional dynamics; even when the dynamics contains lower-dimensional attractors there is almost never a coordinate system available in which the
出版日期Book 2001
关键词Monte Carlo method; Time series; behavior; data analysis; dynamical systems; modeling; nonlinear dynamics;
版次1
doihttps://doi.org/10.1007/978-1-4612-0177-9
isbn_softcover978-1-4612-6648-8
isbn_ebook978-1-4612-0177-9
copyrightSpringer Science+Business Media New York 2001
The information of publication is updating

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发表于 2025-3-21 21:18:14 | 显示全部楼层
Book 2001ok describes the current state of the art of telling useful lies about time-varying systems in the real world. Specifically, it is about trying to "understand" (that is, tell useful lies about) dynamical systems directly from observa­ tions, either because they are too complex to model in the conven
发表于 2025-3-22 04:24:46 | 显示全部楼层
Removing the Noise from Chaos Plus Noisehe underlying dynamical system admits bomoclinic pairs. It is also shown that consistent signal extraction is possible when the errors are uniformly bounded by a suitable constant and the underlying dynamical system has the “weak orbit separation property”. Simple algorithms for signal recovery are described in the latter case.
发表于 2025-3-22 06:27:13 | 显示全部楼层
Consistent Estimation of a Dynamical Mapn the second, dynamical noise model, the system is perturbed by independent noise between each application of F. Estimates of F are proposed for each model, and are shown to be consistent under general conditions. No assumptions are made regarding mixing rates of the observations. Both continuous and general measurable maps F are considered.
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Formulas for the Eckmann-Ruelle Matrixted Jacobian, which we call the Eckmann-Ruelle matrix, reflects details of the embedding rather than the underlying dynamics. We establish formulas for the expected values of the entries of the Eckmann-Ruelle matrix, in both the presence and absence of observational noise.
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Data Compression, Dynamics, and Stationarityto estimate many of the usual dynamically interesting quantities such as topological entropy. They are also well-suited for a specific new application: testing the stationarity of time-series of discrete symbols, whether two data streams appear to originate from the same underlying unknown dynamical system.
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Noise and Nonlinearity in an Ecological Systemto their physical environment. Such models provide better forecasts than can be achieved with conventional linear techniques and identify processes hidden to linear analysis. The importance of understanding the interplay between noise and nonlinearity in ecological systems is discussed.
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