Translational and nontranslational motion of perturbed Turing patterns

When the front and rear boundaries of a Turing pattern with nonzero flux boundary conditions move synchronously, several modes of motion of the pattern are found. Traveling boundaries can be obtained experimentally by illuminating a Turing-unstable system through a moving mask consisting of a single dark stripe with a light intensity sufficient to suppress pattern formation. All structured moving patterns belong to two general types: smooth translation at low mask velocity v(x) and nontranslational ("hopping") at intermediate v(x). At high v(x), Turing patterns are unable to form, and an unstructured striped image of the mask is seen. When the mask width exceeds the Turing wavelength, bistability between different types of moving patterns can occur as v(x) is varied.