Spiral waves linear and nonlinear theory / Björn Sandstede, Arnd Scheel.
| Author/creator | Sandstede, Björn |
| Other author | Scheel, Arnd, 1966- |
| Format | Electronic |
| Publication Info | Providence, RI : American Mathematical Society, 2023. |
| Description | v, 126 pages : illustrations ; 26 cm. |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Subjects |
| Series | Memoirs of the American Mathematical Society, 0065-9266 ; volume 285, number 1413 (third of 6 numbers) |
| Abstract | "Spiral waves are striking self-organized coherent structures that organize spatiotemporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather than studying existence in a specific equation, we study properties of spiral waves in general reaction-diffusion systems. We show that many features of spiral waves are robust and to some extent independent of the specific model analyzed. To accomplish this, we present a suitable analytic framework, spatial radial dynamics, that allows us to rigorously characterize features such as the shape of spiral waves and their eigenfunctions, properties of the linearization, and finite-size effects. We believe that our framework can also be used to study spiral waves further and help analyze bifurcations, as well as provide guidance and predictions for experiments and numerical simulations. From a technical point of view, we introduce non-standard function spaces for the well-posedness of the existence problem which allow us to understand properties of spiral waves using dynamical systems techniques, in particular exponential dichotomies. Using these pointwise methods, we are able to bring tools from the analysis of one-dimensional coherent structures such as fronts and pulses to bear on these inherently two-dimensional defects"-- Provided by publisher. |
| Bibliography note | Includes bibliographical references (pages 119-123) and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2023023511 |
| ISBN | 9781470463090 (paperback) |
| ISBN | (pdf) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |