Radially Symmetric Patterns of Reaction-Diffusion Systems

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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.

Original languageEnglish (US)
JournalMemoirs of the American Mathematical Society
Issue number786
StatePublished - Sep 2003


  • Center manifolds
  • Defects
  • Normal forms
  • Reaction-diffusion systems
  • Target patterns


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