Keywords
Bifurcation theory, Dynamics, Geometry, Algebraic, Toric varieties
Abstract
The dynamics of (bio) chemical reaction networks have been studied by different methods. Among these methods, the chemical reaction network theory has been proven to successfully predicate important qualitative properties, such as the existence of the steady state and the asymptotic behavior of the steady state. However, a constructive approach to the steady state locus has not been presented. In this thesis, with the help of toric geometry, we propose a generic strategy towards this question. This theory is applied to (bio)nano particle configurations. We also investigate Hopf bifurcation surfaces of various dynamical systems.
Notes
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Graduation Date
2011
Semester
Summer
Advisor
Brennan, Joseph P.
Degree
Doctor of Philosophy (Ph.D.)
College
College of Sciences
Department
Mathematics
Format
application/pdf
Identifier
CFE0003933
URL
http://purl.fcla.edu/fcla/etd/CFE0003933
Language
English
Release Date
August 2011
Length of Campus-only Access
None
Access Status
Doctoral Dissertation (Open Access)
STARS Citation
Chen, Teng, "Algebraic Aspects of (Bio) Nano-chemical Reaction Networks and Bifurcations in Various Dynamical Systems" (2011). Electronic Theses and Dissertations. 6647.
https://stars.library.ucf.edu/etd/6647