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Open Physics

formerly Central European Journal of Physics

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Volume 13, Issue 1


Volume 13 (2015)

Novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis

Dragutin T. Mihailović
  • Corresponding author
  • Faculty of Agriculture, University of Novi Sad, Dositeja Obradovica Sq. 8, 21000 Novi Sad, Serbia
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Gordan Mimić
  • Faculty of Sciences, Department of Physics, University of Novi Sad, Dositeja Obradovica Sq. 3, 21000 Novi Sad, Serbia
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Emilija Nikolić-Djorić / Ilija Arsenić
Published Online: 2014-09-25 | DOI: https://doi.org/10.1515/phys-2015-0001


We propose novel metrics based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We consider the origins of the Kolmogorov complexity and discuss its physical meaning. To get better insights into the nature of complex systems and time series analysis we introduce three novel measures based on the Kolmogorov complexity: (i) the Kolmogorov complexity spectrum, (ii) the Kolmogorov complexity spectrum highest value and (iii) the overall Kolmogorov complexity. The characteristics of these measures have been tested using a generalized logistic equation. Finally, the proposed measures have been applied to different time series originating from: a model output (the biochemical substance exchange in a multi-cell system), four different geophysical phenomena (dynamics of: river flow, long term precipitation, indoor 222Rn concentration and UV radiation dose) and the economy (stock price dynamics). The results obtained offer deeper insights into the complexity of system dynamics and time series analysis with the proposed complexity measures.

Keywords : complexity; physical complexity; Kolmogorov complexity spectrum; overall Kolmogorov complexity; time series

PACS : ; ; ; ;


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About the article

Received: 2013-03-11

Accepted: 2014-06-24

Published Online: 2014-09-25

Published in Print: 2015-01-01

Citation Information: Open Physics, Volume 13, Issue 1, ISSN (Online) 2391-5471, DOI: https://doi.org/10.1515/phys-2015-0001.

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© 2015 D. T. Mihailovic et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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