Turing Pattern Formation in the Chlorine Dioxide-Iodine-Malonic Acid Reaction-Diffusion System
The formation of localized structures in the chlorine dioxide-idodine-malonic acid (CDIMA) reaction-diffusion system is investigated numerically using a realistic model of this system. We analyze the one-dimensional patterns formed along the gradients imposed by boundary feeds, and study their linear stability to symmetry-breaking perturbations (the Turing instability) in the plane transverse to these gradients. We establish that an often-invoked simple local linear analysis which 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 experimental results. We also verify that the two-variable reduction of the chemical model employed in the linear stability analysis is justified. Finally, we present numerical solution of the CDIMA system in two dimensions which is in qualitative agreement with experiments. This result also confirms our linear stability analysis, while demonstrating the feasibility of numerical exploration of realistic chemical models.