Instabilities and spatio-temporal chaos in hexagon patterns with rotation

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–Bénard 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 wave numbers.