Chaos and strange attractors of the lorenz equations

This research introduces and analyzes the famous Lorenz equations which are a classical example of a dynamical continuous system exhibiting chaotic behavior. This system is a three-dimensional system of first order autonomous differential equations and their dynamics are quite complicated. Some basi...

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Main Author:	Salim, Nurul Hidayah
Format:	Thesis
Language:	English
Published:	2014
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/78338/1/NurulHidayahSalimMFS20141.pdf
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id	my-utm-ep.78338
record_format	uketd_dc
spelling	my-utm-ep.783382018-08-26T11:51:55Z Chaos and strange attractors of the lorenz equations 2014-01 Salim, Nurul Hidayah QA Mathematics This research introduces and analyzes the famous Lorenz equations which are a classical example of a dynamical continuous system exhibiting chaotic behavior. This system is a three-dimensional system of first order autonomous differential equations and their dynamics are quite complicated. Some basic dynamical properties, such as stability, bifurcations, chaos and attractor are studied, either qualitatively or quantitatively. The visualization of the strange attractor and chaotic orbit are displayed using phase portrait and also the time series graph. A way to detect the chaotic behavior of an orbit is by using the Lyapunov exponents which indicate chaoticity if there is at least one positive Lyapunov exponent. The Lyapunov dimension called Kaplan-Yorke dimension of the chaotic attractor of this system is calculated to prove the strangeness by non-integer number. Several visualization methods are applied to this system to help better understand the long time behavior of the system. This is achieved by varying the parameters and initial conditions to see the kind of behavior induced by the Lorenz equations. The mathematical algebra softwares, Matlab and Maple, are utilized to facilitate the study. Also, the compound structure of the butterfly-shaped attractor named Lorenz attractor is also explored. 2014-01 Thesis http://eprints.utm.my/id/eprint/78338/ http://eprints.utm.my/id/eprint/78338/1/NurulHidayahSalimMFS20141.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:80018 masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Salim, Nurul Hidayah Chaos and strange attractors of the lorenz equations
description	This research introduces and analyzes the famous Lorenz equations which are a classical example of a dynamical continuous system exhibiting chaotic behavior. This system is a three-dimensional system of first order autonomous differential equations and their dynamics are quite complicated. Some basic dynamical properties, such as stability, bifurcations, chaos and attractor are studied, either qualitatively or quantitatively. The visualization of the strange attractor and chaotic orbit are displayed using phase portrait and also the time series graph. A way to detect the chaotic behavior of an orbit is by using the Lyapunov exponents which indicate chaoticity if there is at least one positive Lyapunov exponent. The Lyapunov dimension called Kaplan-Yorke dimension of the chaotic attractor of this system is calculated to prove the strangeness by non-integer number. Several visualization methods are applied to this system to help better understand the long time behavior of the system. This is achieved by varying the parameters and initial conditions to see the kind of behavior induced by the Lorenz equations. The mathematical algebra softwares, Matlab and Maple, are utilized to facilitate the study. Also, the compound structure of the butterfly-shaped attractor named Lorenz attractor is also explored.
format	Thesis
qualification_level	Master's degree
author	Salim, Nurul Hidayah
author_facet	Salim, Nurul Hidayah
author_sort	Salim, Nurul Hidayah
title	Chaos and strange attractors of the lorenz equations
title_short	Chaos and strange attractors of the lorenz equations
title_full	Chaos and strange attractors of the lorenz equations
title_fullStr	Chaos and strange attractors of the lorenz equations
title_full_unstemmed	Chaos and strange attractors of the lorenz equations
title_sort	chaos and strange attractors of the lorenz equations
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2014
url	http://eprints.utm.my/id/eprint/78338/1/NurulHidayahSalimMFS20141.pdf
_version_	1747817964858507264

Chaos and strange attractors of the lorenz equations

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