Abstract
Optical pattern formation in a spin-$1/2$ atomic system is theoretically studied in the situation of interaction between the Hopf and static instabilities. Variation of the parameters of the system permits a drastic change of the ratio between the spatial wave numbers of the Hopf and the static modes. If the mode coupling satisfies spatiotemporal phase matching conditions, regular patterns in the form of triadic Hopf-static patterns or oscillating patterns with hexagonal symmetry (``winking hexagons'') are formed. Otherwise, the simultaneous excitement of the Hopf and static modes leads to the development of spatiotemporal turbulence that is in agreement with results obtained in other systems.
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