Description
- Abstract:
- Abstract of Homoclinic Snaking of Spatiotemporal Patterns in Reaction Diffusion Equations, by Timothy V Roberts, Ph.D., Brown University, May 2024. Spiral and target waves are features of many models of two or more components on 2-dimensional domains driven by diffusion. This is true of many phenomena, including: the electrochemical behavior of the heart, oxidation patterns on platinum alloys, and populations of slime molds. In each of these cases, one can experimentally observe the existence and competition of these patterns. However, the theory behind their existence, stability and interaction is enormously complicated and not fully understood. In this work, we have used rigorous geometric techniques to prove that “1-dimensional” spirals and targets, known as contact defect solutions, exist under certain general assumptions. Moreover, we have established a general framework that makes qualitative and quantitative predictions about the nature of the bifurcation diagrams of these patterns. These so called snaking bifurcations have remarkably complex features which we are able to understand through the combination of classical homoclinic snaking and spatial dynamical systems.
- Notes:
- Thesis (Ph. D.)--Brown University, 2024
Citation
Roberts, Timothy Victor,
"Homoclinic Snaking of Spatiotemporal Patterns in Reaction Diffusion Systems"
(2024).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:y8vdpd2h/
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Collection:
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Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....