Spatiotemporal reaction-diffusion patterns emerging on cylindrical surfaces due to global coupling

A condensed polynomial model, that captures the main features of high- or l ow-pressure catalytic oscillations, is used to simulate spatiotemporal patt erns in a cylindrical catalytic surface. This model includes a single autoc atalytic variable (activator) and a slow changing and localized inhibitor s ubject to a global interaction mechanism which maintains the spatial averag e of the activator at the set point. While for very short (small length L) or very narrow (small perimeter P) cylinders the pattern preserves the stru ctures of the corresponding one-dimensional problems (a ring or a wire), tw o-dimensional patterns emerge for comparable L and P showing a large multip licity of spatiotemporal behavior because of a very high sensivity to initi al conditions. The effect of kinetic parameters and system size is studied. Approximate solutions for the bifurcation from one- to two-dimension patte rns are derived. (C) 2001 American Institute of Physics.