Eur. Phys. J. Special Topics 222, 421-436 (2013)
https://doi.org/10.1140/epjst/e2013-01850-y

Regular Article

Permutation complexity of interacting dynamical systems

¹ Max-Planck-Institut für extraterrestrische Physik, Giessenbachstr. 1, 85748 Garching, Germany
² Centro de Investigación Operativa, Universidad Miguel Hernandez, Avda. de la Universidad s/n, 03202 Elche, Spain

^a e-mail: monetti@mpe.mpg.de

Received: 27 March 2013
Revised: 25 April 2013
Published online: 25 June 2013

Abstract

The coupling complexity index is an information measure introduced within the framework of ordinal symbolic dynamics. This index is used to characterize the complexity of the relationship between dynamical system components. In this work, we clarify the meaning of the coupling complexity by discussing in detail some cases leading to extreme values, and present examples using synthetic data to describe its properties. We also generalize the coupling complexity index to the multivariate case and derive a number of important properties by exploiting the structure of the symmetric group. The applicability of this index to the multivariate case is demonstrated with a real-world data example. Finally, we define the coupling complexity rate of random and deterministic time series. Some formal results about the multivariate coupling complexity index have been collected in an Appendix.