Predictability of Chaotic Dynamics

A Finite-time Lyapunov Exponents Approach

Juan C. Vallejo, Miguel A. F. Sanjuan (Autoren)

Buch | Hardcover

XV, 136 Seiten

2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-51892-3 (ISBN)

Infos

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.

Autor

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.

Inhalt

Preface.- Forecasting and Chaos.- Lyapunov Exponents.- Dynamical Regimes and Timescales.- Predictability.- Numerical Calculation of Lyapunov Exponents.

Produkt-Details

• Erscheinungsdatum: 03.06.2017
• Reihe/Serie: Springer Series in Synergetics
• Zusatzinfo: XV, 136 p. 47 illus., 22 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Maße: 155 x 235 mm
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
• Schlagworte: Applications of Nonlinear Dynamics and Chaos Theor • astronautics • Dynamics and statics • Finite Lyapunov exponents • Finite-time exponent distribution • Forecasting in chaotic systems • Henon-Heiles system • Mathematical Applications in the Physical Sciences • Mathematical Modelling • Mathematical Physics • Nonlinear Science • Numerical and Computational Physics, Simulation • Physics • Physics and Astronomy • Simulation of galactic dynamics • Space Sciences (including Extraterrestrial Physics
• ISBN-10: 3-319-51892-5 / 3319518925
• ISBN-13: 978-3-319-51892-3 / 9783319518923
• Zustand: Neuware