The University of Southampton
University of Southampton Institutional Repository

Understanding chaotic dissipative dynamics in the State Space with Fuzzy Systems

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
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.

Record type: Conference or Workshop Item (Other)

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.

This record has no associated files available for download.

More information

Published date: March 1996
Additional Information: Address: Plymouth
Venue - Dates: International Conference on Adaptive Computing in Engineering Design and Control '96, , Plymouth, United Kingdom, 1996-03-01
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 250005
URI: http://eprints.soton.ac.uk/id/eprint/250005
PURE UUID: c44752e2-48d8-4e58-9584-86fc0ad2cd6a

Catalogue record

Date deposited: 04 May 1999
Last modified: 10 Dec 2021 20:06

Export record

Contributors

Author: T.E. Schilhabel
Author: C.J. Harris

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×