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• W577588936 abstract "This thesis describes three applications of the theory of continuous autonomous dynamicalsystems. The focus of the thesis is on qualitative, as opposed to numerical, analysis. Theapplications examined are biological and chemical, and as such there are signi�cant uncertaintiesin any mathematical representation of them. While the qualitative relationshipsthat de�ne a biological or chemical system may be well understood, it is often di�cultto obtain accurate measurements of the parameters that govern each interaction, due toinherent variability and/or experimental constraints. For this reason, a model that avoidsdependence on numerical values while still accurately re�ecting the qualitative structure ofthe system it represents is potentially of use in gaining a greater understanding of how thesystem can behave. Conversely, if a purely qualitative model allows certain behaviour thatis never experimentally observed, this may highlight the importance of certain parametervalues for the system's real world behaviour.The �rst application presented is a model of electron transport in mitochondria, the secondis a model of an inter-cellular gap junction, and the third represents a set of reactionsoccurring in a continuous �ow stirred tank reactor. For each application, a reasonableset of qualitative assumptions is found under which there is a unique steady state towhich all initial conditions converge, regardless of precise numerical values. Uniquenessof steady states is proved using results on the injectivity of functions, and degree theory.The convergence criteria are constructed using two di�erent areas of dynamical systemstheory. The �rst of these is the theory of monotone �ows, while the second is a group ofresults known as �autonomous convergence theorems�. The theory of monotone �ows isfairly well known, and relies on �nding conditions under which trajectories of a dynamicalsystem preserve a partial ordering, thereby limiting the possibly asymptotic behaviour ofthe system. The autonomous convergence theorems appear much less well known; theywork by �nding a norm under which trajectories approach each other, either in phase spaceor in a related exterior algebra space. Both theories are discussed in detail, along withsome extensions." @default.
• W577588936 created "2016-06-24" @default.
• W577588936 creator A5012101452 @default.
• W577588936 date "2009-04-01" @default.
• W577588936 modified "2023-09-26" @default.
• W577588936 title "Stability and robust behaviour across classes of biological and chemical models" @default.
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• W577588936 hasPublicationYear "2009" @default.
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