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.