The European Physical Journal Special Topics

, Volume 222, Issue 2, pp 363–381

A new perspective on transcripts by means of their matrix representation

Some properties and applications to coupled systems
  • W. Bunk
  • J.M. Amigó
  • T. Aschenbrenner
  • R. Monetti
Regular Article Theoretical Aspects II: Coupling

DOI: 10.1140/epjst/e2013-01847-6

Cite this article as:
Bunk, W., Amigó, J., Aschenbrenner, T. et al. Eur. Phys. J. Spec. Top. (2013) 222: 363. doi:10.1140/epjst/e2013-01847-6

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.

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  • W. Bunk
    • 1
  • J.M. Amigó
    • 2
  • T. Aschenbrenner
    • 1
  • R. Monetti
    • 1
  1. 1.Max-Planck-Institut für extraterrestrische PhysikGarching b. MünchenGermany
  2. 2.Centro de Investigacion Operativa, Universidad Miguel HernandezElcheSpain