Transverse instabilities in chemical Turing patterns of stripes

Abstract

We present a theoretical and experimental study of the sideband instabilities in Turing patterns of stripes. We compare numerical computations of the Brusselator model with experiments in a chlorine dioxide–iodine– malonic acid ~CDIMA! reaction in a thin gel layer reactor in contact with a continuously refreshed reservoir of reagents. Spontaneously evolving Turing structures in both systems typically exhibit many defects that break the symmetry of the pattern. Therefore, the study of sideband instabilities requires a method of forcing perfect, spatially periodic Turing patterns with the desired wave number. This is easily achieved in numerical simulations. In experiments, the photosensitivity of the CDIMA reaction permits control and modulation of Turing structures by periodic spatial illumination with a wave number outside the stability region. When a too big wave number is imposed on the pattern, the Eckhaus instability may arise, while for too small wave numbers an instability sets in forming zigzags. By means of the amplitude equation formalism we show that, close to the hexagon-stripe transitions, these sideband instabilities may be preceded by an amplitude instability that grows transient spots locally before reconnecting with stripes. This prediction is tested in both the reaction-diffusion model and the experiment.