Understanding chaotic dissipative dynamics in the State Space with Fuzzy Systems
Understanding chaotic dissipative dynamics in the State Space with Fuzzy Systems
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 explicitly given crisp boxes and their attached probabilities, when the resolution of the fuzzy sets is fine enough. After summarizing 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.
Schilhabel, T.E.
616a5112-bbe1-4d55-a6f3-2a70f6dfc011
Harris, C.J.
c4fd3763-7b3f-4db1-9ca3-5501080f797a
March 1996
Schilhabel, T.E.
616a5112-bbe1-4d55-a6f3-2a70f6dfc011
Harris, C.J.
c4fd3763-7b3f-4db1-9ca3-5501080f797a
Schilhabel, T.E. and Harris, C.J.
(1996)
Understanding chaotic dissipative dynamics in the State Space with Fuzzy Systems.
International Conference on Adaptive Computing in Engineering Design and Control '96, , Plymouth, United Kingdom.
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Abstract
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 explicitly given crisp boxes and their attached probabilities, when the resolution of the fuzzy sets is fine enough. After summarizing 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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Published date: March 1996
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Address: Plymouth
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International Conference on Adaptive Computing in Engineering Design and Control '96, , Plymouth, United Kingdom, 1996-03-01
Organisations:
Southampton Wireless Group
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Local EPrints ID: 250005
URI: http://eprints.soton.ac.uk/id/eprint/250005
PURE UUID: c44752e2-48d8-4e58-9584-86fc0ad2cd6a
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Date deposited: 04 May 1999
Last modified: 10 Dec 2021 20:06
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Author:
T.E. Schilhabel
Author:
C.J. Harris
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