Stability of rolls and hexagonal patterns in non-potential systems

The stability of rolls, hexagons and non-equilateral hexagonal patterns is considered in the framework of a system of amplitude equations containing non-potential resonant quadratic terms. The stability analysis of roll patterns reveals a new kind of instability which can generate steady non-equilateral hexagons, noise-sensitive transitions between roll patterns or periodic oscillations. The Busse balloons for equilateral and non-equilateral hexagons are calculated.