Chaos from simple models to complex systems

Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introductio...

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Hlavní autoři: Cencini, Massimo, Cecconi, Fabio, Vulpiani, Angelo
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: New Jersey World Scientific Publishing Co. Pte. Ltd 2010
World Scientific
World Scientific Publishing Company
WORLD SCIENTIFIC
WSPC
Edice:Series on advances in statistical mechanics
Témata:
All Nonlinear Science Titles
BioMathematics
Biostatistics
Chaotic behavior in systems
Dynamics
Mathematical Computation and Modeling
Mathematical Physics
SCIENCE
Statistical Physics, Complexity and Nonlinear Dynamical Systems
Chaos
Dynamical Systems
Information Theory
Spatiotemporal Chaos
Applications of Chaos
Statistical Dynamics
Modeling
Complexity
ISBN:9789814277655, 9814277657, 9789814277662, 9814277665, 9813203587, 9789813203587
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Abstract Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology.
AbstractList Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology.The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations.The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses.Sample Chapter(s)Introduction (164 KB)Chapter 1: First Encounter with Chaos (1,323 KB)Contents: First Encounter with ChaosThe Language of Dynamical SystemsExamples of Chaotic BehaviorsProbabilistic Approach to ChaosCharacterization of Chaotic Dynamical SystemsFrom Order to Chaos in Dissipative SystemsChaos in Hamiltonian SystemsChaos and Information TheoryCoarse-Grained Information and Large Scale PredictabilityChaos in Numerical and Laboratory ExperimentsChaos in Low Dimensional SystemsSpatiotemporal ChaosTurbulence as a Dynamical System ProblemChaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case StudyReadership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses.
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology.
Author Cecconi, Fabio
Vulpiani, Angelo
Cencini, Massimo
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Keywords Chaos
Dynamical Systems
Information Theory
Spatiotemporal Chaos
Applications of Chaos
Statistical Dynamics
Modeling
Complexity
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Notes Includes bibliographical references (p. 427-454) and index
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SubjectTerms All Nonlinear Science Titles
BioMathematics
Biostatistics
Chaotic behavior in systems
Dynamics
Mathematical Computation and Modeling
Mathematical Physics
SCIENCE
Statistical Physics, Complexity and Nonlinear Dynamical Systems
SubjectTermsDisplay Chaotic behavior in systems
Dynamics
Subtitle from simple models to complex systems
TableOfContents Chaos : from simple models to complex systems -- Preface -- Introduction -- Contents -- Part 1: Introduction to Dynamical Systems and Chaos -- Chapter 1: First Encounter with Chaos -- Chapter 2: The Language of Dynamical Systems -- Chapter 3: Examples of Chaotic Behaviors -- Chapter 4: Probabilistic Approach to Chaos -- Chapter 5: Characterization of Chaotic Dynamical Systems -- Chapter 6: From Order to Chaos in Dissipative Systems -- Chapter 7: Chaos in Hamiltonian Systems -- Part 2: Advanced Topics and Applications: From Information Theory to Turbulence -- Chapter 8: Chaos and Information Theory -- Chapter 9: Coarse-Grained Information and Large Scale Predictability -- Chapter 10: Chaos in Numerical and Laboratory Experiments -- Chapter 11: Chaos in Low Dimensional Systems -- Chapter 12: Spatiotemporal Chaos -- Chapter 13: Turbulence as a Dynamical System Problem -- Chapter 14: Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study -- Epilogue -- Bibliography -- Index.
Title Chaos
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