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This paper studies analytically and numerically the role of the homogeneous zero mode on the interaction between two subcritical modulation instabilities with the same critical wavelength. For this purpose, this study considers a passive cavity with plane mirrors filled by a resonant two-level medium, and driven by an injected plane wave beam. This work assumes a weak dispersion, where the dynamics is described by the Swift-Hohenberg type of equation. It constitutes a paradigm for the study of both periodic and localized patterns formation.