Current Search: bifurcation theory (x)
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Title
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SOLITARY WAVE FAMILIES IN TWO NON-INTEGRABLE MODELS USING REVERSIBLE SYSTEMS THEORY.
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Creator
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Leto, Jonathan, Choudhury, S. Roy, University of Central Florida
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Abstract / Description
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In this thesis, we apply a recently developed technique to comprehensively categorize all possible families of solitary wave solutions in two models of topical interest. The models considered are: a) the Generalized Pochhammer-Chree Equations, which govern the propagation of longitudinal waves in elastic rods, and b) a generalized microstructure PDE. Limited analytic results exist for the occurrence of one family of solitary wave solutions for each of these equations. Since, as mentioned...
Show moreIn this thesis, we apply a recently developed technique to comprehensively categorize all possible families of solitary wave solutions in two models of topical interest. The models considered are: a) the Generalized Pochhammer-Chree Equations, which govern the propagation of longitudinal waves in elastic rods, and b) a generalized microstructure PDE. Limited analytic results exist for the occurrence of one family of solitary wave solutions for each of these equations. Since, as mentioned above, solitary wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions of both models here (via the normal form approach) within the framework of reversible systems theory. Besides confirming the existence of the known family of solitary waves for each model, we find a continuum of delocalized solitary waves (or homoclinics to small-amplitude periodic orbits). On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solitons. For the microstructure equation, the new family of solutions occur in regions of parameter space distinct from the known solitary wave solutions and are thus entirely new. Directions for future work, including the dynamics of each family of solitary waves using exponential asymptotics techniques, are also mentioned.
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Date Issued
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2008
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Identifier
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CFE0002151, ucf:47930
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Format
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Document (PDF)
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PURL
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http://purl.flvc.org/ucf/fd/CFE0002151
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Title
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ALGEBRAIC ASPECTS OF (BIO) NANO-CHEMICAL REACTION NETWORKS AND BIFURCATIONS IN VARIOUS DYNAMICAL SYSTEMS.
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Creator
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Chen, Teng, Brennan, Joseph, University of Central Florida
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Abstract / Description
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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...
Show moreThe 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 con gurations. We also investigate Hopf bifurcation surfaces of various dynamical systems.
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Date Issued
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2011
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Identifier
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CFE0003933, ucf:48689
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Format
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Document (PDF)
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PURL
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http://purl.flvc.org/ucf/fd/CFE0003933
