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Permutation Complexity in Dynamical Systems: Ordinal Patterns, Permutation Entropy and All That: Springer Series in Synergetics

Autor José Amigó
en Limba Engleză Paperback – 4 mai 2012
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.
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Specificații

ISBN-13: 9783642262890
ISBN-10: 3642262899
Pagini: 268
Ilustrații: X, 280 p. 13 illus. in color.
Dimensiuni: 155 x 235 x 14 mm
Greutate: 0.39 kg
Ediția:2010
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Springer Series in Synergetics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

What Is This All About?.- First Applications.- Ordinal Patterns.- Ordinal Structure of the Shifts.- Ordinal Structure of the Signed Shifts.- Metric Permutation Entropy.- Topological Permutation Entropy.- Discrete Entropy.- Detection of Determinism.- Space–Time Dynamics.- Conclusion and Outlook.

Recenzii

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)

Textul de pe ultima copertă

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.

Caracteristici

Includes supplementary material: sn.pub/extras