Studies in chaos using stochastic methods
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Authors
Healy, Edward A.
Subjects
chaos
Lorenz
duffing
fractal dimension
multivariate scaling analysis
Lorenz
duffing
fractal dimension
multivariate scaling analysis
Advisors
Kolar, Ramesh
Date of Issue
1991-06
Date
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
Methods of chaos have been used to classify many heretofore inexplicable nonlinear dynamical systems in fields as diverse as ecology to engineering and economics to meteorology. This thesis presents the mathematical background needed to understand chaos as well as the engineering techniques used to study the nature of dynamical systems. Several dynamical systems are studied using two probabilistic measures of chaos, fractal correlation dimension and the multivariate scaling analysis. A new technique for developing a multivariate scaling analysis using a time embedding procedure is presented. The dynamical systems studied include the Lorenz equations, Duffing's equation and helicopter flight vibrations
Type
Thesis
Description
Series/Report No
Department
Aeronautical Engineering
Organization
Naval Postgraduate School
Identifiers
NPS Report Number
Sponsors
Funder
Format
75 p.;28 cm.
Citation
Distribution Statement
Approved for public release; distribution is unlimited.