Convergence analysis of the Brain-state-in-a-Box(BSB) model with delay

In this paper, theoretical analysis proves the convergence properties of the brain-state-in-a-box (BSB) models with delay. We propose a convergence theorem of the BSB with delay, generalized the BSB without delay, while all previous studies on this model without delay assumed that symmetric and quasi-symmetric. We have performed a detailed convergence analysis of this network and found convergence theorem under proper assumptions of the weight matrices of this network. One is non-symmetric and the other is row diagonal dominant. Meanwhile, 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 its updating rate is four times higher than that of the original BSB.