Nonlinear Dynamics

, Volume 89, Issue 2, pp 1385–1395 | Cite as

Complexity measure by ordinal matrix growth modeling

  • J. S. Armand Eyebe FoudaEmail author
  • Wolfram Koepf
Original Paper


We present a new approach based on the modeling of the behavior of the number of ordinal matrices derived from time series, as a function of the embedding dimension. We show that the number of distinct ordinal matrices can be used for determining whether the dynamics are regular or chaotic by means of the periodicity (\(\mu \)), quasiperiodicity (\(\alpha \)) and nonregularity (\(\lambda \)) index herein defined. We verify that \(\lambda \) behaves similarly to the Lyapunov exponent and therefore can be used for measuring complexity in time series whose underlying equations are unknown. Moreover, the combination of \(\mu \), \(\alpha \) and \(\lambda \) enables us to distinguish between deterministic and stochastic data. We thus propose the variation law of the number of ordinal matrices characterizing the random walk.


Complexity Ordinal matrix Lyapunov exponent Time series 



This work was supported by the Alexander von Humboldt Foundation (Grant No. KAM 1133622).


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Physics, Faculty of ScienceUniversity of Yaoundé IYaoundéCameroon
  2. 2.Institute of MathematicsUniversity of KasselKasselGermany

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