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.
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http://homepage.tudelft.nl/19j49/Matlab_Toolbox_for_Dimensionality_Reduction.html
Martens, H.: The Informative Converse paradox: Windows into the unknown. Chemometrics and Intelligent Laboratory Systems, 124–138 (2011)
Johnson, R.A., Wichern, D.W.: Applied Multivariate Statistical Analysis. Prentice Hall, London (2007)
Pearson, K.: On lines and planes of closest fit to systems of points in space. Philosophical Magazine 2, 559–572 (1901)
Viswanath, D.: The fractal property of the Lorenz attractor. J. Atmos. Sci. 20, 130–141 (1963)
Lorenz, E.N.: Deterministic nonperiodic flow. Physica D 190, 115–128 (2004)
Zampa, P., Arnost, R.: 4th WSEAS Conference (2004)
Grassberger, P., Procaccia, P.: Characterization of Strange Attractors. Phys. Rev. Lett. 50, 346–349 (1983)
Grassberger, P., Procaccia, P.: Measuring the strangeness of strange attractors. Physica D 9, 189–208 (1983)
Stys, D., http://www.expertomica.eu/software.php
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)
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)
Urban, J., Vanek, J., Stys, D.: Preprocessing of microscopy images via Shannon’s entropy. Pattern Recognition and Information Processing, 283–187 (2009)
Jalnine et al, arXiv:0805.0118v1
Zahri, M.: Numerical Solutions of a Stochastic Lorenz Attractor. J. Num. Mat. Stoch. 2, 1–11 (2010)
Wilensky, M.: NetLogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL (1999), http://ccl.northwestern.edu/netlogo/
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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
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DOI: https://doi.org/10.1007/978-3-642-28583-7_4
Publisher Name: Springer, Berlin, Heidelberg
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