Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
Book cover

International Workshop on Self-Organizing Systems

IWSOS 2012: Self-Organizing Systems pp 36–47Cite as

  1. Home
  2. Self-Organizing Systems
  3. Conference paper
On Measurement of Internal Variables of Complex Self-Organized Systems and Their Relation to Multifractal Spectra

On Measurement of Internal Variables of Complex Self-Organized Systems and Their Relation to Multifractal Spectra

  • Dalibor Štys18,
  • Petr Jizba19,
  • Štěpán Papáček18,
  • Tomáš Náhlík18 &
  • …
  • Petr Císař18 
  • Conference paper
  • 949 Accesses

  • 3 Citations

Part of the Lecture Notes in Computer Science book series (LNCCN,volume 7166)

Abstract

We propose a method for characterizing structured, experimentally observable, complex self-organized systems. The method in question is based on the observation that number of self-organized systems can be mathematically perceived as consisting of several interconnected multifractal components. We illustrate our key results with ensuing applications. The relation of the results obtained to known examples of strange attractors is also discussed.

Keywords

  • Rényi entropy
  • principal component analysis
  • generalized dimensions
  • multifractal spectra

Download conference paper PDF

References

  1. http://homepage.tudelft.nl/19j49/Matlab_Toolbox_for_Dimensionality_Reduction.html

  2. Martens, H.: The Informative Converse paradox: Windows into the unknown. Chemometrics and Intelligent Laboratory Systems, 124–138 (2011)

    Google Scholar 

  3. Johnson, R.A., Wichern, D.W.: Applied Multivariate Statistical Analysis. Prentice Hall, London (2007)

    MATH  Google Scholar 

  4. Pearson, K.: On lines and planes of closest fit to systems of points in space. Philosophical Magazine 2, 559–572 (1901)

    Google Scholar 

  5. Viswanath, D.: The fractal property of the Lorenz attractor. J. Atmos. Sci. 20, 130–141 (1963)

    CrossRef  Google Scholar 

  6. http://www.camo.com/

  7. Lorenz, E.N.: Deterministic nonperiodic flow. Physica D 190, 115–128 (2004)

    CrossRef  MathSciNet  Google Scholar 

  8. Zampa, P., Arnost, R.: 4th WSEAS Conference (2004)

    Google Scholar 

  9. Grassberger, P., Procaccia, P.: Characterization of Strange Attractors. Phys. Rev. Lett. 50, 346–349 (1983)

    CrossRef  MathSciNet  Google Scholar 

  10. Grassberger, P., Procaccia, P.: Measuring the strangeness of strange attractors. Physica D 9, 189–208 (1983)

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Stys, D., http://www.expertomica.eu/software.php

  12. Stys, D., Vanek, J., Nahlik, T., Urban, J., Cisar, P.: The cell monolayer trajectory from the system state point of view. Mol. BioSyst. 7, 2824–2833 (2011)

    CrossRef  Google Scholar 

  13. Stys, D., Urban, J., Vanek, J., Cisar, P.: Analysis of biological time-lapse microscopic experiment from the point of view of the information theory. Micron. 41, 478–483 (2010)

    CrossRef  Google Scholar 

  14. Urban, J., Vanek, J., Stys, D.: Preprocessing of microscopy images via Shannon’s entropy. Pattern Recognition and Information Processing, 283–187 (2009)

    Google Scholar 

  15. Jalnine et al, arXiv:0805.0118v1

    Google Scholar 

  16. Zahri, M.: Numerical Solutions of a Stochastic Lorenz Attractor. J. Num. Mat. Stoch. 2, 1–11 (2010)

    MathSciNet  Google Scholar 

  17. Wilensky, M.: NetLogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL (1999), http://ccl.northwestern.edu/netlogo/

Download references

Author information

Authors and Affiliations

  1. School of Complex Sytems, Faculty of Fishery and Water Protection, University of South Bohemia, Zámek 136, 373 33, Nové Hrady, Czech Republic

    Dalibor Štys, Štěpán Papáček, Tomáš Náhlík & Petr Císař

  2. FNSPE, Czech Technical University in Prague, Břehová 7, 115 19, Prague, Czech Republic

    Petr Jizba

Authors
  1. Dalibor Štys
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Petr Jizba
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Štěpán Papáček
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tomáš Náhlík
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Petr Císař
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    Fernando A. Kuipers

  2. Department of Telematics, Norwegian University of Science and Technology, O.S. Bragstads plass 2B, 7491, Trondheim, Norway

    Poul E. Heegaard

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 IFIP International Federation for Information Processing

About this paper

Cite this paper

Štys, D., Jizba, P., Papáček, Š., Náhlík, T., Císař, P. (2012). On Measurement of Internal Variables of Complex Self-Organized Systems and Their Relation to Multifractal Spectra. In: Kuipers, F.A., Heegaard, P.E. (eds) Self-Organizing Systems. IWSOS 2012. Lecture Notes in Computer Science, vol 7166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28583-7_4

Download citation

  • .RIS
  • .ENW
  • .BIB
  • DOI: https://doi.org/10.1007/978-3-642-28583-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28582-0

  • Online ISBN: 978-3-642-28583-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature