Pattern formation near an oscillatory instability for systems without up-down symmetry

We present the results of our numerical investigations of the order parameter equation associated with an oscillatory instability with a small onset frequency of systems lacking up-down symmetry. Qualitatively different patterns arise depending on whether periodic or more realistic boundary conditions are used. Among the patterns found are blinking hexagons, traveling rectangular patterns, and states that are disordered in space and time, which dominate for realistic boundary conditions. Experimentally accessible systems for which our predictions could be checked might include non-Boussinesq convection in binary fluid mixtures. © 1997 Elsevier Science B.V.