Download or read book Radially Symmetric Patterns of Reaction-diffusion Systems written by Arnd Scheel and published by American Mathematical Soc.. This book was released on 2003 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.