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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
http://eprints.utm.my/id/eprint/78338/
http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:80018
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spelling my.utm.783382018-08-26T11:51:55Z http://eprints.utm.my/id/eprint/78338/ Chaos and strange attractors of the lorenz equations 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 NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/78338/1/NurulHidayahSalimMFS20141.pdf Salim, Nurul Hidayah (2014) Chaos and strange attractors of the lorenz equations. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science. http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:80018
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
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
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
publishDate 2014
url http://eprints.utm.my/id/eprint/78338/1/NurulHidayahSalimMFS20141.pdf
http://eprints.utm.my/id/eprint/78338/
http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:80018
_version_ 1643657867659575296
score 13.211869

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