Optimal Network Interventions to Control the Spreading of Oscillations

Oscillations are a prominent feature of neuronal activity and are associated with a variety of phenomena in brain tissue, both healthy and unhealthy. Characterizing how oscillations spread through regions of the brain is of particular interest when studying countermeasures to pathological brain synchronizations. This paper models neuronal activity using networks of interconnected excitatory-inhibitory pairs with linear threshold dynamics, and presents strategies to design networks with desired robustness properties. In particular, we develop a dynamical description of the brain through a network where the state of each node models the firing rate of a region of neurons and where edges capture the structural connectivity between the regions. We characterize the presence of oscillations and study conditions on their spreading. We also discuss strategies to optimally design networks which are robust to oscillation spreading. We demonstrate our results with numerical simulations.