LOCALIZED STRUCTURES AND FRONT PROPAGATION IN THE LENGYEL-EPSTEIN MODEL

Pattern selection, localized structure formation, and front propagatio n are analyzed within the framework of a model for the chlorine dioxid e-iodine-malonic acid reaction that represents a key to understanding recently obtained Turing structures. This model is distinguished from previously studied, simple reaction-diffusion models by producing a st rongly subcritical transition to stripes. The wave number for the mode s of maximum linear gain is calculated and compared with the dominant wave number for the finally selected, stationary structures grown from the homogeneous steady state or developed behind a traveling front. T he speed of propagation for a front between the homogeneous steady sta te and a one-dimensional (ID) Turing structure is obtained. This veloc ity shows a characteristic change in behavior at the crossover between the subcritical and supercritical regimes for the Turing bifurcation. In the subcritical regime there is an interval where the front veloci ty vanishes as a result of a pinning of the front to the underlying st ructure. In 2D, two different nucleation mechanisms for hexagonal stru ctures are illustrated on the Lengyel-Epstein and the Brusselator mode l. Finally, the observation of ID and 2D spirals with Turing-induced c ores is reported.