Turing instability in a boundary-fed system

The formation of localized structures in the chlorine dioxide-idodine-malonic acid ~CDIMA! reactiondiffusion system is investigated numerically using a realistic model of this system. We analyze the onedimensional patterns formed along the gradients imposed by boundary feeds, and study their linear stability to symmetry-breaking perturbations ~Turing instability! in the plane transverse to these gradients. We establish that an often-invoked simple local linear analysis that neglects longitudinal diffusion is inappropriate for predicting the linear stability of these patterns. Using a fully nonuniform analysis, we investigate the structure of the patterns formed along the gradients and their stability to transverse Turing pattern formation as a function of the values of two control parameters: the malonic acid feed concentration and the size of the reactor in the dimension along the gradients. The results from this investigation are compared with existing experiments. @S1063-651X~98!15009-2#