Practical Approach to Construction of Internal Variables of Complex Self-organized Systems and Its Theoretical Foundation

  • Dalibor ŠtysEmail author
  • Petr Jizba
  • Tomáš Náhlík
  • Karina Romanova
  • Anna Zhyrova
  • Petr Císař
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


We propose a method for characterizing the image—multidimensional projection—of complex, self-organising, system. The method is general and may be used for characterisation of any structured, experimentally observable, complex self-organized systems. The method is based on calculation of information gain by which a point contributes to the total information in the image, the point information gain, PIG. We have also derived related variables, the point information gain entropy PIE and point information gain entropy density PIED. The later values are unique to a structured information and may be used for analysis of similarity by clustering, identification of states etc. We illustrate our key results using the example of living cell. We discuss practical limits of the analogy between this observable self-organising system and its possible theoretical model using an example of chaotic attractor.


Rényi entropy Point information gain Principal component analysis Principal manifold Chaotic attractor 



This work was partly supported and co-financed by the South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses (CZ.1.05/2.1.00/01.0024) and by the Grant Agency of the University of South Bohemia (152/2010/Z 2012).


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Dalibor Štys
    • 1
    Email author
  • Petr Jizba
    • 2
  • Tomáš Náhlík
    • 1
  • Karina Romanova
    • 1
  • Anna Zhyrova
    • 1
  • Petr Císař
    • 1
  1. 1.School of Complex Systems, FFPWUniversity of South BohemiaNové HradyCzech Republic
  2. 2.FNSPECzech Technical University in PraguePragueCzech Republic

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