| eBook ISBN: | 978-1-4704-0384-3 |
| Product Code: | MEMO/165/786.E |
| List Price: | $60.00 |
| MAA Member Price: | $54.00 |
| AMS Member Price: | $36.00 |
| eBook ISBN: | 978-1-4704-0384-3 |
| Product Code: | MEMO/165/786.E |
| List Price: | $60.00 |
| MAA Member Price: | $54.00 |
| AMS Member Price: | $36.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 165; 2003; 86 ppMSC: Primary 35; 37; 34
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.
ReadershipGraduate students and research mathematicians interested in differential equations.
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Table of Contents
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Chapters
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1. Introduction
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2. Instabilities in one space dimension
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3. Stationary radially symmetric patterns
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4. Time-periodic radially symmetric patterns
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5. Discussion
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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.
-
Chapters
-
1. Introduction
-
2. Instabilities in one space dimension
-
3. Stationary radially symmetric patterns
-
4. Time-periodic radially symmetric patterns
-
5. Discussion
