Sufficient Conditions for Oscillations in Competitive Linear-Threshold Brain Networks

Oscillatory activity is highly prevalent in the brain. Oscillations with specific characteristics are associated with a variety of healthy and diseased brain functions. This letter considers two mesoscale brain network models described by linear-threshold and threshold-linear dynamics and takes on the analytical characterization of the emergence of oscillations. The synaptic connectivity is described by an arbitrary network interconnection topology that allows for self-excitatory nodes. We provide a structural characterization for the existence of stable node sets that support asymptotically stable equilibria and identify sufficient conditions for oscillatory behavior in competitive linear-threshold and threshold-linear dynamics. Simulations illustrate our results.