Deformed Hexagonal Patterns in a Weakly Anisotropic System

(Received 16 July 1996, revised 21 November 1996, accepted 8 January 1997)

Abstract
For a two-dimensional model of pattern formation the interplay between a broken up down symmetry and a weakly broken rotational symmetry is investigated. Both symmetries may be broken, for instance, in chemical reactions with an applied electric field or in thermal convection of planarly aligned nematic liquid crystals. In a system with rotational symmetry and a broken up down symmetry hexagonal patterns are favored in a certain parameter range. With increasing values for the anisotropies, by keeping the up down symmetry broken, hexagons may be deformed to centered rectangular patterns. Hence, breaking both symmetries is an alternative mechanism leading to rectangular patterns. Finally, at larger values of the anisotropies a bifurcation to stripes takes place.