Eur. Phys. J. Special Topics 222, 553-568 (2013)
https://doi.org/10.1140/epjst/e2013-01859-2

Regular Article

Identification of equivalent dynamics using ordinal pattern distributions

¹ Max-Planck-Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
² Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen, Germany
³ Department of Physics and Astronomy, Graduate School of Science and Engineering, Kagoshima University, 1-21-35 Korimto Kagoshima 890-0065, Japan
⁴ Decoding and Controlling Brain Information, PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi 332-0012, Japan
⁵ Flucto-Order Functions Research Team, RIKEN–HYU Collaboration Research Center, 2-1 Hirosawa, Wako 351-0198, Japan

^a e-mail: ulrich.parlitz@ds.mpg.de

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

Abstract

The frequency of occurrence of ordinal patterns in an observed (or measured) times series can be used to identify equivalent dynamical system. We demonstrate this approach for system identification and parameter estimation for dynamics that can (at least approximately) be described by one-dimensional iterated maps.