Hierarchical Selective Recruitment in Linear-Threshold Brain Networks Part II: Multilayer Dynamics and Top-Down Recruitment

Goal-driven selective attention (GDSA) is a remarkable function that allows the complex dynamical networks of brain to support coherent perception and cognition. Part I this two-part article proposes new control-theoretic framework, termed hierarchical recruitment (HSR), rigorously explain emergence GDSA from brain's network structure dynamics. This part completes development HSR by deriving conditions on joint subnetworks guarantee top-down task-relevant each subnetwork at layer immediately above, while inhibiting activity task-irrelevant all layers. To further verify merit applicability we carry out comprehensive case study listening in rodents show small with HSR-based can data accuracy satisfying theoretical stability timescale separation requirements HSR. Our technical approach relies theory switched systems provides novel converse Lyapunov theorem for state-dependent affine independent interest.