Localized structures and front propagation in the Lengyel-Epstein model

Pattern selection, localized structure formation, and front propagation are analyzed within the framework of a model for the chlorine dioxide–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 strongly subcritical transition to stripes. The wave number for the modes 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. The speed of propagation for a front between the homogeneous steady state and a one-dimensional (1D) Turing structure is obtained. This velocity 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 velocity vanishes as a result of a pinning of the front to the underlying structure. In 2D, two different nucleation mechanisms for hexagonal structures are illustrated on the Lengyel-Epstein and the Brusselator model. Finally, the observation of 1D and 2D spirals with Turing-induced cores is reported.