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 n on-potential resonant quadratic terms. The stability analysis of roll patte rns reveals a new kind of instability which can generate steady non-equilat eral hexagons, noise-sensitive transitions between roll patterns or periodi c oscillations. The Busse balloons for equilateral and non-equilateral hexa gons are calculated. (C)2000 Elsevier Science B.V. All rights reserved.