In a previous paper [Kilmer (1996) Neural Netw 9: 567-573] we developed a differential equation model of how a stable focus of attention could be maintained in a higher mammalian brain. The so-called TRC model consisted of interconnected modules, with each module comprised of a simple representations of parts of the reticular thalamic nucleus, specific thalamic nuclei, nonspecific thalamic nuclei, and cortex, together with the known excitatory and inhibitory interconnections between them. TRC was analyzed only for steady states under zero inputs. Here we analyze the behavior of TRC_2, a substantially modified and reinterpreted TRC, for steady attention and attention-switching behavior under nonzero inputs. We show that TRC_2 always converges to a unique mode of primary attention, and that it allows concurrently one or more other modes of weak attention, which experience suggests occurs often. A crucial postulate for TRC_2 is that a mode alpha does not actively compete against other modes unless primary attention is paid to mode alpha. This postulate should be testable experimentally.