- Title Information
- Title
- Homoclinic Snaking of Spatiotemporal Patterns in Reaction Diffusion Systems
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Roberts, Timothy Victor
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Sandstede, Bjorn
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Beck, Margaret
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Menon, Govind
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2024
- Physical Description
- Extent
- xiv, 135 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2024
- Genre (aat)
- theses
- 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.
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00893484")
- Topic
- Differential equations, Partial
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01400410")
- Topic
- Applied mathematics
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01055244")
- Topic
- Pattern formation (Biology)
- Subject
- Topic
- dynamical systems
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20240502