Eur. Phys. J. Special Topics 222, 363-381 (2013)
https://doi.org/10.1140/epjst/e2013-01847-6

Regular Article

A new perspective on transcripts by means of their matrix representation

Some properties and applications to coupled systems

¹ Max-Planck-Institut für extraterrestrische Physik, 85740 Garching b. München, Germany
² Centro de Investigacion Operativa, Universidad Miguel Hernandez, Avda. de la Universidad s/n, 03202 Elche, Spain

^a e-mail: wolfram.bunk@mpe.mpg.de

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

Abstract

Transcripts map the ordinal pattern representation of e.g. one time series onto another (coupled) one by carrying out permutations. Their representation in terms of permutation matrices motivates the use of elements of linear algebra to derive properties that are of interest for the characterization of coupled dynamical systems. In this contribution, we summarize a number of these properties from a theoretical point of view, in particular those resulting from the application of algebraic techniques, such as eigenvalue calculations, to averaged transition matrices. Finally, we test this approach on data from mathematical models of coupled systems and on a real world data set.