  The dynamics of hexagon patterns in rotating systems are investigated within
the framework of modified Swift-Hohenberg equations that can be considered as
simple models for rotating convection with broken up-down symmetry, e.g.
non-Boussinesq Rayleigh-Benard or Marangoni convection. In the weakly nonlinear
regime a linear stability analysis of the hexagons reveals long- and short-wave
instabilities, which can be steady or oscillatory. The oscillatory short-wave
instabilities can lead to stable hexagon patterns that are periodically
modulated in space and time, or to a state of spatio-temporal chaos with a
Fourier spectrum that precesses on average in time. The chaotic state can
exhibit bistability with the steady hexagon pattern. There exist regimes in
which the steady hexagon patterns are unstable at all wavenumbers.
