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Algebraic Aspects Of (Bio) Nano-Chemical Reaction Networks And Bifurcations In Various Dynamical Systems, Teng Chen
Electronic Theses and Dissertations
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.
Variational Embedded Solitons, And Traveling Wavetrains Generated By Generalized Hopf Bifurcations, In Some Nlpde Systems, Todd Blanton Smith
Variational Embedded Solitons, And Traveling Wavetrains Generated By Generalized Hopf Bifurcations, In Some Nlpde Systems, Todd Blanton Smith
Electronic Theses and Dissertations
In this Ph.D. thesis, we study regular and embedded solitons and generalized and degenerate Hopf bifurcations. These two areas of work are seperate and independent from each other. First, variational methods are employed to generate families of both regular and embedded solitary wave solutions for a generalized Pochhammer PDE and a generalized microstructure PDE that are currently of great interest. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in …