Analysis of Chaotic Behavior in Non-linear Dynamical Systems
Models and Algorithms for Quaternions
Authors: Piórek, Michał
Free Preview- Introduces the first analysis of chaos in the processes described by quaternions
- Provides an analysis of chaotic behavior in non-linear dynamical systems using models and algorithms of quaternions
- Includes methods that allow not only the detection of deterministic chaos in quaternion time series but also the classification of the nature of the dynamical system, which drives the quaternion time series
- Proposes methodology to identify three types of the quaternion time series: random, periodic, and chaotic
- Brings additional value by proposing a framework of quaternion clustering, which includes the proposition of a quaternions clustering algorithm along with the measures of the quaternions clustering validity
- Tests the quality of quaternion clustering against three parameters of the input data set: real clusters number, overlapping degree, and variance of the data set
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- About this book
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This book presents a new approach for the analysis of chaotic behavior in non-linear dynamical systems, in which output can be represented in quaternion parametrization. It offers a new family of methods for the analysis of chaos in the quaternion domain along with extensive numerical experiments performed on human motion data and artificial data. All methods and algorithms are designed to allow detection of deterministic chaos behavior in quaternion data representing the rotation of a body in 3D space. This book is an excellent reference for engineers, researchers, and postgraduate students conducting research on human gait analysis, healthcare informatics, dynamical systems with deterministic chaos or time series analysis.
- Table of contents (10 chapters)
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Introduction
Pages 1-5
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Processes Described by Quaternion Models
Pages 7-17
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Deterministic Chaos Properties
Pages 19-34
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Analysis of Chaos from Time Series - Existing Methods Survey
Pages 35-43
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Analysis of Chaos from Quaternion Time Series - Proposed Methods
Pages 45-64
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Table of contents (10 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Analysis of Chaotic Behavior in Non-linear Dynamical Systems
- Book Subtitle
- Models and Algorithms for Quaternions
- Authors
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- Michał Piórek
- Series Title
- Studies in Systems, Decision and Control
- Series Volume
- 160
- Copyright
- 2019
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing AG, part of Springer Nature
- eBook ISBN
- 978-3-319-94887-4
- DOI
- 10.1007/978-3-319-94887-4
- Hardcover ISBN
- 978-3-319-94886-7
- Softcover ISBN
- 978-3-030-06931-5
- Series ISSN
- 2198-4182
- Edition Number
- 1
- Number of Pages
- XI, 132
- Number of Illustrations
- 27 b/w illustrations, 71 illustrations in colour
- Topics
