In pattern-forming systems the wave-number bands accessible to the system are drastically reduced if the control parameters are varied slowly in space from supercritical to subcritical. Using a recently derived matching condition, these wave-number bands are calculated in a simple model for Taylor vortex flow. They show qualitatively the same behavior as observed in the experiments on this system: (1) starting from a minimal bandwidth, the band grows both for decreasing as well as increasing control parameter ε; and (2) the dependence of the selected wave number on the system length shows a phase shift of half a wavelength during the crossover from small-ε to large-ε behavior. These results are in quantitative agreement with a numerical simulation of the model.

• Received 9 July 1987

DOI:https://doi.org/10.1103/PhysRevA.37.636