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Radially Symmetric Patterns of Reaction-Diffusion Systems
Arnd Scheel, University of Minnesota, Minneapolis, MN

Memoirs of the American Mathematical Society
2003; 86 pp; softcover
Volume: 165
ISBN-10: 0-8218-3373-1
ISBN-13: 978-0-8218-3373-5
List Price: US$60
Individual Members: US$36
Institutional Members: US$48
Order Code: MEMO/165/786
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In this paper, bifurcations of stationary and time-periodic solutions to reaction-diffusion systems are studied. We develop a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns. In particular, we show the existence of localized pulses near saddle-nodes, critical Gibbs kernels in the cusp, focus patterns in Turing instabilities, and active or passive target patterns in oscillatory instabilities.


Graduate students and research mathematicians interested in differential equations.

Table of Contents

  • Introduction
  • Instabilities in one space dimension
  • Stationary radially symmetric patterns
  • Time-periodic radially symmetric patterns
  • Discussion
  • Bibliography
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