Quantifying Chaos from Time-series Data Through Lyapunov Exponents
Quantifying Chaos from Time-series Data Through Lyapunov Exponents

Author: Julio Emilio Sandubete Galán

Publisher:

Published: 2020

Total Pages:

ISBN-13:

DOWNLOAD EBOOK

Chaos theory has been hailed as a revolution of thoughts and attracting ever increasing attention of many scientists from diverse disciplines. Chaotic systems are nonlinear deterministic dynamic systems which can behave like an apparently erratic and irregular motion. Keep in mind that if we could characterise a chaotic system in some sense it would allow us to evidence that a deterministic generating system exists behind that chaotic system in spite of showing an apparently random behaviour. This fact would provide us to take advantage of this deterministic character to be able to make predictions and control over the variables of these (chaotic) deterministic dynamic systems. Methods and techniques related to test the hypothesis of chaos try to estimate the so-called Lyapunov exponents as a way of characterising achaotic system. Nowadays quantifying chaos from time-series data through this kind of quantitative measure in a rigorous fashion is far from being a trivial exercise and poses a number of theoretical and practical challenges...

Nonlinearities in Economics
Nonlinearities in Economics

Author: Giuseppe Orlando

Publisher: Springer Nature

Published: 2021-08-31

Total Pages: 361

ISBN-13: 3030709825

DOWNLOAD EBOOK

This interdisciplinary book argues that the economy has an underlying non-linear structure and that business cycles are endogenous, which allows a greater explanatory power with respect to the traditional assumption that dynamics are stochastic and shocks are exogenous. The first part of this work is formal-methodological and provides the mathematical background needed for the remainder, while the second part presents the view that signal processing involves construction and deconstruction of information and that the efficacy of this process can be measured. The third part focuses on economics and provides the related background and literature on economic dynamics and the fourth part is devoted to new perspectives in understanding nonlinearities in economic dynamics: growth and cycles. By pursuing this approach, the book seeks to (1) determine whether, and if so where, common features exist, (2) discover some hidden features of economic dynamics, and (3) highlight specific indicators of structural changes in time series. Accordingly, it is a must read for everyone interested in a better understanding of economic dynamics, business cycles, econometrics and complex systems, as well as non-linear dynamics and chaos theory.

Nonlinear Time Series Analysis
Nonlinear Time Series Analysis

Author: Holger Kantz

Publisher: Cambridge University Press

Published: 2004

Total Pages: 390

ISBN-13: 9780521529020

DOWNLOAD EBOOK

The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.

Chaos Detection and Predictability
Chaos Detection and Predictability

Author: Charalampos (Haris) Skokos

Publisher: Springer

Published: 2016-03-04

Total Pages: 280

ISBN-13: 3662484102

DOWNLOAD EBOOK

Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data. In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists. The book covers theoretical and computational aspects of traditional methods to calculate Lyapunov exponents, as well as of modern techniques like the Fast (FLI), the Orthogonal (OFLI) and the Relative (RLI) Lyapunov Indicators, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), the Smaller (SALI) and the Generalized (GALI) Alignment Index and the ‘0-1’ test for chaos.

Measuring Chaos In The Human Brain - Proceedings Of The Conference
Measuring Chaos In The Human Brain - Proceedings Of The Conference

Author: Dennis W Duke

Publisher: World Scientific

Published: 1991-10-31

Total Pages: 266

ISBN-13: 9814555983

DOWNLOAD EBOOK

This conference brought together scientists from diverse disciplines such as biomedical and electrical engineering, mathematics, physics, neurology, neuroscience, psychophysiology and psychology to discuss the application of nonlinear dynamics in the study of brain function. This is a relatively new field which involves measuring the properties of chaotic strange attractors in the human EEG. Probably the earliest and still most exciting result in the field is that 'the more chaos the better' is the rule in many physiological areas. We have only the most speculative ideas about why the brain might be chaotic and what the implications are if it really is. The potential is unimaginably large. This volume will serve to inspire others to pursue research in this field and point the way in some promising directions.

Chaos and Time-series Analysis
Chaos and Time-series Analysis

Author: Julien C. Sprott

Publisher: Oxford University Press, USA

Published: 2003

Total Pages: 507

ISBN-13: 9780198508397

DOWNLOAD EBOOK

This text provides an introduction to the exciting new developments in chaos and related topics in nonlinear dynamics, including the detection and quantification of chaos in experimental data, fractals, and complex systems. Most of the important elementary concepts in nonlinear dynamics arediscussed, with emphasis on the physical concepts and useful results rather than mathematical proofs and derivations. While many books on chaos are purely qualitative and many others are highly mathematical, this book fills the middle ground by giving the essential equations, but in the simplestpossible form. It assumes only an elementary knowledge of calculus. Complex numbers, differential equations, and vector calculus are used in places, but those tools are described as required. The book is aimed at the student, scientist, or engineer who wants to learn how to use the ideas in apractical setting. It is written at a level suitable for advanced undergraduate and beginning graduate students in all fields of science and engineering.

International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2004)
International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2004)

Author: Theodore Simos

Publisher: CRC Press

Published: 2019-04-29

Total Pages: 1192

ISBN-13: 1482284200

DOWNLOAD EBOOK

The International Conference of Computational Methods in Sciences and Engineering (ICCMSE) is unique in its kind. It regroups original contributions from all fields of the traditional Sciences, Mathematics, Physics, Chemistry, Biology, Medicine and all branches of Engineering. The aim of the conference is to bring together computational scientists from several disciplines in order to share methods and ideas. More than 370 extended abstracts have been submitted for consideration for presentation in ICCMSE 2004. From these, 289 extended abstracts have been selected after international peer review by at least two independent reviewers.

Analysis of Observed Chaotic Data
Analysis of Observed Chaotic Data

Author: Henry Abarbanel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 278

ISBN-13: 1461207630

DOWNLOAD EBOOK

A clear and systematic treatment of time series of data, regular and chaotic, found in nonlinear systems. The text leads readers from measurements of one or more variables through the steps of building models of the source as a dynamical system, classifying the source by its dynamical characteristics, and finally predicting and controlling the dynamical system. It examines methods for separating the signal of physical interest from contamination by unwanted noise, and for investigating the phase space of the chaotic signal and its properties. The emphasis throughout is on the use of modern mathematical tools for investigating chaotic behaviour to uncover properties of physical systems, requiring knowledge of dynamical systems at the advanced undergraduate level and some knowledge of Fourier transforms and other signal processing methods.

Statistical Physics and Chaos in Fusion Plasmas
Statistical Physics and Chaos in Fusion Plasmas

Author: C. W. Horton, Jr.

Publisher: Wiley-Interscience

Published: 1984-04-24

Total Pages: 392

ISBN-13:

DOWNLOAD EBOOK

Papers from twenty-nine of the world's leading scientists investigate the statistical properties of nonlinear dynamical systems, emphasizing their relation to the problem of plasma confinement. A powerful, new diagrammatic peturbation theory is presented for a first principles calculation of the Clump Kinetic equation, and for the first time, detailed calculations and experimental considerations describe the practical consequences of these correlations. Unique to this book is the collection of works on the problem of long-lived correlations in phase space of the Vlasov Poisson system. A new method of computing Lyapunov exponents from experimental data, and a method for calculating the splitting of periodic orbits in conservative systems are developed.

Chaos and Nonlinear Dynamics
Chaos and Nonlinear Dynamics

Author: Robert C. Hilborn

Publisher:

Published: 2000

Total Pages: 676

ISBN-13: 9780198507239

DOWNLOAD EBOOK

This book introduces readers to the full range of current and background activity in the rapidly growing field of nonlinear dynamics. It uses a step-by-step introduction to dynamics and geometry in state space to help in understanding nonlinear dynamics and includes a thorough treatment of both differential equation models and iterated map models as well as a derivation of the famous Feigenbaum numbers. It is the only introductory book available that includes the important field of pattern formation and a survey of the controversial questions of quantum chaos. This second edition has been restructured for easier use and the extensive annotated references are updated through January 2000 and include many web sites for a number of the major nonlinear dynamics research centers. With over 200 figures and diagrams, analytic and computer exercises this book is a necessity for both the classroom and the lab.