Predictability of chaotic dynamics : a finite-time Lyapunov exponents approach / Juan C. Vallejo, Miguel A.F. Sanjuan.
Vallejo, Juan C., author.; Sanjuán, Miguel A. F. (Miguel Angel Fernández), author.
2017
Q172.5.C45
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Title
Predictability of chaotic dynamics : a finite-time Lyapunov exponents approach / Juan C. Vallejo, Miguel A.F. Sanjuan.
Author
Vallejo, Juan C., author.
ISBN
9783319518930 (electronic book)
3319518933 (electronic book)
9783319518923
3319518925
DOI
https://doi.org/10.1007/978-3-319-51893-0
Published
Cham, Switzerland : Springer, 2017.
Language
English
Description
1 online resource.
Item Number
10.1007/978-3-319-51893-0 doi
Call Number
Q172.5.C45
Dewey Decimal Classification
003/.857
Summary
This book is primarily concerned with the computational aspects of predictability of dynamical systems - in particular those where observation, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, for instance in celestial mechanics, one is confronted with the observation and modeling of systems without the possibility of altering the key parameters of the objects studied. Therefore, the numerical simulations offer an essential tool for analyzing these systems. With the widespread use of computer simulations to solve complex dynamical systems, the reliability of the numerical calculations is of ever-increasing interest and importance. This reliability is directly related to the regularity and instability properties of the modeled flow. In this interdisciplinary scenario, the underlying physics provide the simulated models, nonlinear dynamics provides their chaoticity and instability properties, and the computer sciences provide the actual numerical implementation. This book introduces and explores precisely this link between the models and their predictability characterization based on concepts derived from the field of nonlinear dynamics, with a focus on the finite-time Lyapunov exponents approach. The method is illustrated using a number of well-known continuous dynamical systems, including the Contopoulos, Hénon-Heiles and Rössler systems. To help students and newcomers quickly learn to apply these techniques, the appendix provides descriptions of the algorithms used throughout the text and details how to implement them in order to solve a given continuous dynamical system.
Bibliography, etc. Note
Includes bibliographical references.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed April 10, 2017).
Added Author
Sanjuán, Miguel A. F. (Miguel Angel Fernández), author.
Series
Springer series in synergetics.
Springer complexity.
Available in Other Form
Predictability of Chaotic Dynamics : A Finite-time Lyapunov Exponents Approach.
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Preface; Contents; Acronyms; 1 Forecasting and Chaos; 1.1 Historical Introduction; 1.1.1 The Scientific Method; 1.1.2 Forecasting and Determinism; 1.2 Chaotic Dynamics; 1.3 Computer Numerical Explorations; 1.3.1 Solving ODEs Numerically; 1.3.2 Numerical Forecast; 1.3.3 Symplectic Integrators; 1.4 Shadowing and Predictability; 1.5 Concluding Remarks; References; 2 Lyapunov Exponents; 2.1 Lyapunov Exponents; 2.2 The Lyapunov Spectrum; 2.3 The Lyapunov Exponents Family; 2.4 Finite-Time Exponents; 2.5 Distributions of Finite-Time Exponents; 2.6 The Harmonic Oscillator; 2.7 The Rössler System.

2.8 The Hénon-Heiles System2.9 Concluding Remarks; References; 3 Dynamical Regimes and Time Scales; 3.1 Temporal Evolution; 3.2 Regimes Identification; 3.3 Transient Behaviours, Sticky Orbits and Transient Chaos; 3.4 The Hénon-Heiles System; 3.5 The Contopoulos System; 3.6 The Rössler System; 3.7 Hyperbolicity Characterisation Through Finite-Time Exponents; 3.8 Concluding Remarks; References; 4 Predictability; 4.1 Numerical Predictability; 4.2 The Predictability Index; 4.2.1 The Hénon-Heiles System; 4.2.2 The Contopoulos System; 4.2.3 The Rössler System; 4.2.4 A Galactic System.

4.3 Concluding RemarksReferences; A Numerical Calculation of Lyapunov Exponents; A.1 The Variational Equation; A.2 Selection of Initial Perturbations; A.3 Other Methods; A.4 Practical Implementation for Building the Finite-Time Distributions; References.

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