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Physico-chemical systems driven away from thermal equilibrium usually undergo various types of instabilities leading to the formation of spatio-temporal patterns on macroscopic time and space scales. In two-dimensional geometries, patterns of different symmetries may be simultaneously stable. We study here the phase stability of hexagonal planforms in the framework of amplitude equations and reduced dynamical models close to the instability points.

The effect of external fields on spatio-temporal Hopf bifurcations is investigated. Left- and right-travelling waves are linearly coupled by uniform oscillations or steady spatial modulations, provided the frequency of the oscillations or the wave number of the modulations are close to two times the critical ones. Hence, a spatially uniform forcing may restore the left-right symmetry by transforming travelling waves into standing waves even in regimes where the latter are otherwise unstable.

The effect of two-dimensional spatial modulations on spatio-temporal Hopf bifurcations is investigated. In particular, in the case of a spatial forcing corresponding to triangular or hexagonal planforms, a strong resonance between triplets of travelling waves may occur, provided that the wavelength of the forcing is nearly equal to one-third of the critical one. In this case a periodic spatio-temporal pattern of triangular symmetry may be stabilized in regions of the parameter space where it is otherwise unstable. Such a phenomenon may present the onset of turbulence in forced hexagonal vortex lattices.