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Radially Symmetric Patterns of Reaction-Diffusion Systems
 
Arnd Scheel University of Minnesota, Minneapolis, MN
Radially Symmetric Patterns of Reaction-Diffusion Systems
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
Radially Symmetric Patterns of Reaction-Diffusion Systems
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Radially Symmetric Patterns of Reaction-Diffusion Systems
Arnd Scheel University of Minnesota, Minneapolis, MN
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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1652003; 86 pp
    MSC: 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.

    Readership

    Graduate students and research mathematicians interested in differential equations.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Instabilities in one space dimension
    • 3. Stationary radially symmetric patterns
    • 4. Time-periodic radially symmetric patterns
    • 5. Discussion
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1652003; 86 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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