Lyapunov exponents: a tool to explore complex dynamics
Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrat…
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- Full title :Lyapunov exponents : a tool to explore complex dynamics / Arkady Pikovsky, University of Potsdam, Antonio Politi, University of Aberdeen.
Summary
Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers.
Read More ↓Edition Statements
- Publication Date:©2016
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:©2016
The Physical Object
- Description:1 online resource (xii, 285 pages)
Edition Identifiers
- ISBN:9781139343473, 1139343475
- oclc:ocn938435075
- LC Classification:QA372
- Dewey Decimal:515/.352
Table of Contents
Introduction -- The basics -- Numerical methods -- Lyapunov vectors -- Fluctuations, finite-time and generalised exponents -- Dimensions and dynamical entropies -- Finite-amplitude exponents -- Random systems -- Coupled systems -- High-dimensional systems: general -- High-dimensional systems: Lyapunov vectors and finite-size effects -- Applications -- Appendices.
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