The existence of SAM mode for the Brain-state-in-a-Box (BSB) models with delay

In this paper, we prove the dynamic properties of the Brain-state-in-a-Box (BSB) models with delay on the Diagonal elements region. The existence domain of SAM (slow active mode) mode is given and the SAM mode is demonstrated to improve the convergence theorem of BSB with delay. The network being considered here is a generalization of traditional BSB, whose initial state is allowed to lie in a general closed convex set. We have illustrated that all next states can be predicted before updating, and the updating process is presented by a newly given updating rule. Theoretical analysis demonstrates that the BSB with delay performs much better than the original one in updating to an equilibrium point, and the less domain of SAM mode is the higher updating rate.