Overview
- Authored by leading researchers in the field
- Self-contained introduction and presentation
- Includes a number of worked-out examples
Part of the book series: Springer Series in Synergetics (SSSYN)
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About this book
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.
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Keywords
Table of contents (5 chapters)
Authors and Affiliations
About the authors
Miguel Sanjuan is full professor of physics at the Universidad Rey Juan Carlos in Madrid, Spain, where he founded the Physics Department in 2006. He is a corresponding member of the Spanish Royal Academy of Sciences, section physics and chemistry, and a foreign member of the Lithuanian Academy of Sciences in the areas of physics and mechanical engineering. Prof. Sanjuan is presently the head of the Nonlinear Dynamics, Chaos and Complex Systems Research Group at the Universidad Rey Juan Carlos.He has published the monograph Nonlinear Resonances (Springer,2015).
Juan C. Vallejo is an astrophysicist working as BepiColombo SGS Software Development Team Leader for the GMV enterprise group at the European Space Astronomy Centre in Madrid. At the same time he collaborates with the Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Fisica, Universidad Rey Juan Carlos.
Juan C. Vallejo is an astrophysicist working as BepiColombo SGS Software Development Team Leader for the GMV enterprise group at the European Space Astronomy Centre in Madrid. At the same time he collaborates with the Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Fisica, Universidad Rey Juan Carlos.
Bibliographic Information
Book Title: Predictability of Chaotic Dynamics
Book Subtitle: A Finite-time Lyapunov Exponents Approach
Authors: Juan C. Vallejo, Miguel A. F. Sanjuan
Series Title: Springer Series in Synergetics
DOI: https://doi.org/10.1007/978-3-319-51893-0
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-84771-9Published: 08 May 2018
eBook ISBN: 978-3-319-51893-0Published: 27 March 2017
Series ISSN: 0172-7389
Series E-ISSN: 2198-333X
Edition Number: 1
Number of Pages: XV, 136
Number of Illustrations: 25 b/w illustrations, 22 illustrations in colour
Topics: Applications of Nonlinear Dynamics and Chaos Theory, Numerical and Computational Physics, Simulation, Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics), Mathematical Applications in the Physical Sciences