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.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/34257 |
| Date | January 2016 |
| Creators | Belzil-Lacasse, Christian |
| Contributors | Leblanc, Victor |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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