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)

Included in

Mathematics Commons

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