Permutation Complexity in Dynamical Systems

Ordinal Patterns, Permutation Entropy and All That

  • José Amigó

Part of the Springer Series in Synergetics book series (SSSYN)

Table of contents

  1. Front Matter
    Pages i-xv
  2. José María Amigó
    Pages 1-28
  3. José María Amigó
    Pages 29-48
  4. José María Amigó
    Pages 49-67
  5. José María Amigó
    Pages 69-83
  6. José María Amigó
    Pages 85-104
  7. José María Amigó
    Pages 105-124
  8. José María Amigó
    Pages 125-145
  9. José María Amigó
    Pages 147-158
  10. José María Amigó
    Pages 159-175
  11. José María Amigó
    Pages 177-194
  12. José María Amigó
    Pages 195-197
  13. Back Matter
    Pages 199-249

About this book


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.


discrete entropy dynamical systems nonlinear dynamics ordinal patterns permutation entropy topological entropy

Authors and affiliations

  • José Amigó
    • 1
  1. 1.Centro de Investigacion OperativaUniversidad Miguel HernandezElcheSpain

Bibliographic information