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Permanent link (DOI): https://doi.org/10.7939/R3ND31

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Stability and Bifurcation Analysis on Delay Differential Equations Open Access

Descriptions

Other title
Subject/Keyword
DDE
two delays
global Hopf bifurcation
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Lin, Xihui
Supervisor and department
Wang, Hao(Department of Mathematical and Statistical Sciences)
Examining committee member and department
Han, Bin(Department of Mathematical and Statistical Sciences)
Ru, Chong-Qing(Department of Mechanical Engeering)
Wang, Hao(Department of Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Applied Mathematics
Date accepted
2012-08-31T12:21:28Z
Graduation date
2012-11
Degree
Master of Science
Degree level
Master's
Abstract
Most recent studies on delay differential equations are mainly focused on local stability analysis, stability switches, and local existence of Hopf bifurcations with only one delay included, while the global existence of Hopf bifurcation and stability analysis with two delays are hardly discussed. In this thesis, we numerically explore global behaviors of Hopf branches arising from where the characteristic roots crossing the imaginary axis, and we reveal that there seems to be a strong and simple underlying rule, which is been partly studied by Li and Shu in their recent paper [Li & Shu 2010a]. In addition, stability analysis on delay differential equations with two discrete delays will also be studied. We extend the work by [Guet al.2005], and establish a similar theory on a more general type of models. Finally, we provide some preliminary results for the two-delay models with parameters depending on one delay.
Language
English
DOI
doi:10.7939/R3ND31
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
Li, M.Y., Lin, X., & Wang, H. (2012) Global Hopf branches of a delayed HTLV-1 infection model: coexistence of multiple attracting limit cycles ( accepted by CAMQ)

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File title: Stability and Bifurcation Analysis on Delay Differential Equations
File author: Xihui Lin
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