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A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a fluid driven by a linear combination of two frequencies. The model exhibits steady-state solutions with 2-, 4-, 6-, and 12-fold symmetric patterns, similar to the periodic and quasiperiodic patterns observed in recent experiments.
Lifshitz et al. (1997) studied this question.