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Institute of Fundamental Sciences
College of Sciences
Pattern formation in reaction-diffusion systems with spatially varying parameters
Different patterns have been observed in nature and living systems, but the mechanisms behind many of these patterns are still unknown; the process is very complex in nature. My research will focus on pattern formation in excitable media like neurons and smooth muscle cells. Excitability of cells occurs as a result of control of the cell volume which causes differences in the concentration of ions (for example Ca2+, K+, Na2+) across the cell membrane, which generates a potential difference across the cell membrane that causes the flow of ionic currents through the ionic channels. This process is modelled mathematically using ordinary differential equations. Our aim is to study the interactions within many cells and how spatiotemporal patterns are formed between many cells. Diffusion and transport of ions between cells are considered; therefore reaction-diffusion equations are used in modelling such problems. However, some of the parameters for the equations may well differ between cells, due to, for example, proximity to some signalling source, which may be a cause of spatiotemporal pattern formation. Hence in this research work, we aim to develop mathematical techniques to study reaction-diffusion systems with spatial parameter variation.
The outcomes of my research will have indirect benefits to people through developing enhanced understanding of mechanisms in human physiology. It will provide a framework for mathematical modelling of such systems. This is an interdisciplinary project and will foster cooperation between different disciplines.
I am from Ogun State in Nigeria. I did my bachelor degree in Industrial Mathematics at the Federal University of Technology, Akure in Nigeria. My research interest focuses on differential equations and modelling, during my master's programme at the African Institute for Mathematical Sciences (AIMS), Ghana I acquired more knowledge in the area of dynamical systems which inspired me to write my thesis on solitons.
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Last updated on Tuesday 04 April 2017