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Qualitative identification of chaotic systems behaviours

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  • Vicha, T.
  • Dohnal, M.

Abstract

There are only three qualitative values positive, negative and zero. This means that there is a maximal number of qualitatively distinguishable scenarios, prescribed by the number of variables and the highest qualitative derivative taken into consideration. There are several chaos related tasks, which can be solved with great difficulties on the numerical level if multidimensional problems are studied. One of them is the identification of all qualitatively different behaviours. To make sure that all distinctive qualitative scenarios are identified a qualitative interpretation of a classical quantitative phase portrait is used. The highest derivatives are usually the second derivatives as it is not possible to safely identify higher derivatives if tasks related to ecology or economics are studied. Two classical models are discussed – Damped oscillation (non chaotic) and Lorenz model (chaotic). There are 191 scenarios of the Lorenz model if only the second derivatives are considered. If the third derivatives are taken into consideration then the number of scenarios is 2619. Complete qualitative results are given in details.

Suggested Citation

  • Vicha, T. & Dohnal, M., 2008. "Qualitative identification of chaotic systems behaviours," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 70-78.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:1:p:70-78
    DOI: 10.1016/j.chaos.2008.01.027
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    Cited by:

    1. Karel Doubravský & Alena Kocmanová & Mirko Dohnal, 2018. "Analysis of Sustainability Decision Trees Generated by Qualitative Models Based on Equationless Heuristics," Sustainability, MDPI, vol. 10(7), pages 1-18, July.
    2. Vicha, T. & Dohnal, M., 2008. "Qualitative feature extractions of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 364-373.
    3. Dohnal, Mirko, 2016. "Complex biofuels related scenarios generated by qualitative reasoning under severe information shortages: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 65(C), pages 676-684.
    4. Doubravsky, Karel & Dohnal, Mirko, 2018. "Qualitative equationless macroeconomic models as generators of all possible forecasts based on three trend values—Increasing, constant, decreasing," Structural Change and Economic Dynamics, Elsevier, vol. 45(C), pages 30-36.

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