  Neuroscientific evidence shows that for most brain networks all pathways
between cortical regions either pass through the thalamus or a transthalamic
parallel route exists for any direct corticocortical connection. This paper
seeks to formally study the dynamical behavior of the resulting thalamocortical
brain networks with a view to characterizing the inhibitory role played by the
thalamus and its benefits. We employ a linear-threshold mesoscale model for
individual brain subnetworks and study both hierarchical and star-connected
thalamocortical networks. Using tools from singular perturbation theory and
switched systems, we show that selective inhibition and recruitment can be
achieved in such networks through a combination of feedback and feedforward
control. Various simulations throughout the exposition illustrate the benefits
resulting from the presence of the thalamus regarding failsafe mechanisms,
required control magnitude, and network performance.
