Analysis of chaotic behavior in non-linear dynamical systems : models and algorithms for quaternions /: models and algorithms for quaternions. (2018)
- Record Type:
- Book
- Title:
- Analysis of chaotic behavior in non-linear dynamical systems : models and algorithms for quaternions /: models and algorithms for quaternions. (2018)
- Main Title:
- Analysis of chaotic behavior in non-linear dynamical systems : models and algorithms for quaternions
- Further Information:
- Note: Michał Piórek.
- Authors:
- Piórek, Michał
- Contents:
- Intro; Acknowledgements; Contents; 1 Introduction; 1.1 Problem Characteristics; 1.2 Proposed Methods and Algorithms, Carried Out Numerical Experiments; 1.3 Novelties Presented in This Work; 1.4 Motivations; 1.5 Book Structure; 2 Processes Described by Quaternion Models; 2.1 Definition of the Processes Described by Quaternion Models; 2.2 Elements of Quaternion's Algebra; 2.3 Quaternions Visualization; 2.4 Quaternions Averaging; 2.5 Quaternions Random Generation; 2.6 Advantages and Disadvantages of Using Quaternions Parametrization of Rotation; 3 Deterministic Chaos Properties 3.1 Dynamical Systems3.2 Chaos Properties; 3.2.1 Positive Entropies; 3.2.2 Strong Sensitivity to Initial Conditions; 3.2.3 Strange Attractor; 3.2.4 Non-integer Fractal Dimension of the Attractor; 3.3 Analysis of Chaos Basing on a Time Series; 3.4 Time Delay Embedding; 4 Analysis of Chaos from Time Series -- Existing Methods Survey; 4.1 Time Delay; 4.2 Embedding Dimension; 4.3 Reconstruction of the Phase Space; 4.4 The Largest Lyapunov's Exponent; 4.5 Entropies; 4.6 Fractal Dimension; 5 Analysis of Chaos from Quaternion Time Series -- Proposed Methods; 5.1 Quaternion's Angle Method 5.2 Time Delay Embedding for Quaternion Time Series5.3 Mutual Information for Quaternions; 5.4 Quaternions Clustering; 5.5 Quaternions Clustering Validity Measures; 5.5.1 Quaternion Davies-Bouldin Index (QDB); 5.5.2 Quaternion Dunn's Index (QDI); 5.5.3 Quaternion Calinski-Harabasz Index (QCH); 5.6 False Nearest Neighbours; 5.7Intro; Acknowledgements; Contents; 1 Introduction; 1.1 Problem Characteristics; 1.2 Proposed Methods and Algorithms, Carried Out Numerical Experiments; 1.3 Novelties Presented in This Work; 1.4 Motivations; 1.5 Book Structure; 2 Processes Described by Quaternion Models; 2.1 Definition of the Processes Described by Quaternion Models; 2.2 Elements of Quaternion's Algebra; 2.3 Quaternions Visualization; 2.4 Quaternions Averaging; 2.5 Quaternions Random Generation; 2.6 Advantages and Disadvantages of Using Quaternions Parametrization of Rotation; 3 Deterministic Chaos Properties 3.1 Dynamical Systems3.2 Chaos Properties; 3.2.1 Positive Entropies; 3.2.2 Strong Sensitivity to Initial Conditions; 3.2.3 Strange Attractor; 3.2.4 Non-integer Fractal Dimension of the Attractor; 3.3 Analysis of Chaos Basing on a Time Series; 3.4 Time Delay Embedding; 4 Analysis of Chaos from Time Series -- Existing Methods Survey; 4.1 Time Delay; 4.2 Embedding Dimension; 4.3 Reconstruction of the Phase Space; 4.4 The Largest Lyapunov's Exponent; 4.5 Entropies; 4.6 Fractal Dimension; 5 Analysis of Chaos from Quaternion Time Series -- Proposed Methods; 5.1 Quaternion's Angle Method 5.2 Time Delay Embedding for Quaternion Time Series5.3 Mutual Information for Quaternions; 5.4 Quaternions Clustering; 5.5 Quaternions Clustering Validity Measures; 5.5.1 Quaternion Davies-Bouldin Index (QDB); 5.5.2 Quaternion Dunn's Index (QDI); 5.5.3 Quaternion Calinski-Harabasz Index (QCH); 5.6 False Nearest Neighbours; 5.7 The Largest Lyapunov's Exponent; 5.8 Correlation Dimension; 6 Numerical Experiments; 6.1 Experiments Description; 6.2 Investigated Time Series; 6.3 Gait Quaternion Time Series; 6.4 Random Quaternion Time Series; 6.5 Periodic Quaternion Time Series 6.6 The Aim of Experiments7 Analysis of Chaos for Quaternion Time Series; 7.1 Analysis of Chaos -- Gait Time Series; 7.1.1 Clusters Number Estimation; 7.1.2 Time Delay Estimation; 7.1.3 Embedding Dimension Estimation; 7.1.4 Phase Space Reconstruction; 7.1.5 The Largest Lyapunov's Exponent Estimation; 7.1.6 Correlation Dimension Estimation; 7.2 Analysis of Chaos -- Periodic Time Series; 7.2.1 Clusters Number Estimation; 7.2.2 Time Delay Estimation; 7.2.3 Embedding Dimension Estimation; 7.2.4 Phase Space Reconstruction; 7.2.5 The Largest Lyapunov Exponent Estimation 7.2.6 Correlation Dimension Estimation7.3 Analysis of Chaos -- Random Time Series; 7.3.1 Clusters Number Estimation; 7.3.2 Time Delay Estimation; 7.3.3 Embedding Dimension Estimation; 7.3.4 Phase Space Reconstruction; 7.3.5 The Largest Lyapunov Exponent Estimation; 7.3.6 Correlation Dimension Estimation; 7.4 Experiments Conclusions; 8 Comparison Against Existing Approaches; 8.1 Compared Approaches; 8.2 Medical Angles Analysis; 8.2.1 Medical Angles Analysis Procedure; 8.2.2 Model Parameters; 8.2.3 LLE Values; 8.3 Quaternion Angles Analysis; 8.3.1 Quaternion Angles Embedding Procedure … (more)
- Publisher Details:
- Cham : Springer
- Publication Date:
- 2018
- Extent:
- 1 online resource
- Subjects:
- 003/.857
Engineering
Mathematical analysis
Chaotic behavior in systems
SCIENCE / System Theory
TECHNOLOGY & ENGINEERING / Operations Research
Chaotic behavior in systems
Mathematical analysis
Science -- Chaotic Behavior in Systems
Nonlinear science
Technology & Engineering -- General
Cybernetics & systems theory
Electronic books - Languages:
- English
- ISBNs:
- 9783319948874
3319948873 - Related ISBNs:
- 9783319948867
3319948865 - Notes:
- Note: Online resource; title from PDF title page (EBSCO, viewed July 19, 2018)
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- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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- Physical Locations:
- British Library HMNTS - ELD.DS.342626
- Ingest File:
- 01_293.xml