Schilhabel, T.E. and Harris, C.J.
Understanding chaotic dissipative dynamics in the State Space with Fuzzy Systems.
Int. Conference on Adaptive Computing in Engineering Design and Control '96
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The introduction gives an overview of chaotic dynamics and their particular properties. The information theoretical approach of unbiased guess, which was proposed by Jaynes, is utilized to derive a probability distribution in the state space. The weighting of parts in the state space by fuzzy sets provides additional information which enables a ``reconstruction'' of probabilities of crisp elements in state spaces without explicitely given crisp boxes and their attached probabilities, when the resolution of the fuzzy sets is fine enough. After summerizing some of the probabilistic quantities for the qualitative description of chaotic maps, a simple example of two fuzzy sets bounded by a crisp interval is employed to demonstrate by comparing the numerical results together with an analytical map, how this approach may be used to calculate probability densities, which are a basic quantity for chaos understanding.
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