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.
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Coullet et al. (1989) studied this question.
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