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Qualitative feature extractions of chaotic systems

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  • Vicha, T.
  • Dohnal, M.

Abstract

The theory of chaos offers useful tools for systems analysis. However, models of complex systems are based on a network of inconsistent, space and uncertain knowledge items. Traditional quantitative methods of chaos analysis are therefore not applicable. The paper by the same authors [Vicha T, Dohnal M. Qualitative identification of chaotic systems behaviours. Chaos, Solitons & Fractals, in press, [Log. No. 601019] ] presents qualitative interpretation of some chaos concepts. There are only three qualitative values positive/increasing, negative/decreasing and zero/constant. It means that any set of qualitative multidimensional descriptions of unsteady state behaviours is discrete and finite. A finite upper limit exists for the total number of qualitatively distinguishable scenarios. A set of 21 published chaotic models is solved qualitatively and 21 sets of all existing qualitative scenarios are presented. The intersection of all 21 scenario sets is empty. There is no such a behaviour which is common for all 21 models. The set of 21 qualitative models (e.g. Lorenz, Rössler) can be used to compare chaotic behaviours of an unknown qualitative model with them to evaluate if its chaotic behaviours is close to e.g. Lorenz chaotic model and how much.

Suggested Citation

  • Vicha, T. & Dohnal, M., 2008. "Qualitative feature extractions of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 364-373.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:2:p:364-373
    DOI: 10.1016/j.chaos.2008.01.008
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    1. Vicha, T. & Dohnal, M., 2008. "Qualitative identification of chaotic systems behaviours," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 70-78.
    2. Gilmore, Claire G., 1993. "A new test for chaos," Journal of Economic Behavior & Organization, Elsevier, vol. 22(2), pages 209-237, October.
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    Cited by:

    1. Wang, Xia, 2009. "Si’lnikov chaos and Hopf bifurcation analysis of Rucklidge system," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2208-2217.

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