Permutation Complexity in Dynamical Systems
Ordinal Patterns, Permutation Entropy and All That
Authors: Amigó, José
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- About this book
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The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems.
Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular regarding the time series analysis of dynamical systems that capitalizes on the order structure of the state space. Indeed, on one hand ordinal patterns and periodic points are closely related, yet ordinal patterns are amenable to numerical methods, while periodicity is not.
Another interesting feature is that since it can be shown that random (unconstrained) dynamics has no forbidden patterns with probability one, their existence can be used as a fingerprint to identify any deterministic origin of orbit generation.
This book is primarily addressed to researchers working in the field of nonlinear dynamics and complex systems, yet will also be suitable for graduate students interested in these subjects. The presentation is a compromise between mathematical rigor and pedagogical approach. Accordingly, some of the more mathematical background needed for more in depth understanding has been shifted into the appendices.
- Reviews
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From the reviews:
“This book describes a study of permutation complexity … . The book is aimed primarily at researchers in nonlinear dynamics and complex systems, but it is also accessible to graduate students.” (William J. Satzer jun, Zentralblatt MATH, Vol. 1197, 2010)
- Table of contents (11 chapters)
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What Is This All About?
Pages 1-28
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First Applications
Pages 29-48
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Ordinal Patterns
Pages 49-67
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Ordinal Structure of the Shifts
Pages 69-83
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Ordinal Structure of the Signed Shifts
Pages 85-104
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Table of contents (11 chapters)
- Download Preface 1 PDF (60.1 KB)
- Download Sample pages 1 PDF (1.1 MB)
- Download Table of contents PDF (52.9 KB)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Permutation Complexity in Dynamical Systems
- Book Subtitle
- Ordinal Patterns, Permutation Entropy and All That
- Authors
-
- José Amigó
- Series Title
- Springer Series in Synergetics
- Copyright
- 2010
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-642-04084-9
- DOI
- 10.1007/978-3-642-04084-9
- Hardcover ISBN
- 978-3-642-04083-2
- Softcover ISBN
- 978-3-642-26289-0
- Series ISSN
- 0172-7389
- Edition Number
- 1
- Number of Pages
- X, 280
- Number of Illustrations
- 13 illustrations in colour
- Topics
