Amanda Elvin

Doctor of Philosophy, (Philosophy in Mathematics)
Study Completed: 2008
College of Sciences


Thesis Title
Pattern formation in a neural field model

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Ms Elvin studied pattern formation in a neural field model that has been used to model working memory for several decades. Prompted by recent research showing a high incidence of gap junctions in areas of the brain where epileptic events are common, she modelled the effects of gap junctions. Ms Elvin undertook research into the formation of different types of spatially localised patterns by applying both analytical and numerical techniques to a partial integro-differential equation. Varying the firing rate characteristics of the neural field produced qualitative changes in solutions. The theory of reversible Hamiltonian systems combined with mathematical neuroscience methods and dynamical systems theory, provided an elegant explanation of the results. Ms Elvin''sresearch makes an important contribution to the development of numerical simulation techniques in the field of mathematical biology.

Professor Carlo Laing
Professor Mick Roberts