The nucleus reticularis thalami, NRT, is a neural sheet draped over the lateral and anterior aspects of the mammalian thalamus. It is situated to play a major role in deciding an animal's modes of attention. We model nonoscillatory aspects of NRT-cortical-thalamic interactions involved in deciding these modes. The model's modules are dynamically aggregated into coupled sets by ongoing brain operations. Global inhibition distributes attention over the sets. A complete mathematical analysis of the model's equilibria and dynamics shows that it has the desired convergent properties.