Study of Dissipative Spots In Three-Component Reaction-Difussion Systems on Two-Dimensional Domains

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Title: Study of Dissipative Spots In Three-Component Reaction-Difussion Systems on Two-Dimensional Domains
Authors: Belzil-Lacasse, Christian
Date: 2016
Abstract: Dissipative spots are found in physical experiments of many branches of natural science. In this thesis we use three-component reaction-diffusion systems on two-dimensional domains in order to generate these patterns. Using a dynamical system approach we proceed with a Fourier analysis on a linearized reaction-diffusion system in order to provide the bifurcation conditions for a given homogeneous state. We validate our results and establish it's limitations through numerical experiments. We report very interesting behavior during these simulations, notably hysteresis and multi-stability. We will then turn our attention to the relatively unexplored phenomenon of rotating spots. Based on previous work done for spiral waves, we investigate the effect of translational symmetry-breaking on a rotating spot mainly through careful numerical analysis.
URL: http://hdl.handle.net/10393/34257
http://dx.doi.org/10.20381/ruor-5458
CollectionThèses, 2011 - // Theses, 2011 -
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