Optimal Network Interventions to Control the Spreading of Oscillations

Abstract

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 excitatoryinhibitory 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.

Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices

“…For instance, social networks, power grids, and computer networks are all examples of networked systems. A large literature has dealt with optimal control of networked systems [55], [56], [57], [58], [59], [60], [61], [62], [63].…”

Vibrational Stabilization of Cluster Synchronization in Oscillator Networks

“…Furthermore, stability conditions for cluster synchronization have been established in networks featuring dyadic connections [9], [17], [18], [19], [20] and hyper connections [21], [22]. To control cluster synchronization, researchers have proposed diverse strategies, such as pinning control [23] and interventions that involve manipulating network connections or the dynamics of individual nodes [24], [25], [26]. In contrast, our approach focuses on vibrational control, which offers a more realistic strategy in many real-world systems, e.g., for regulating neural activity as it resembles deep brain stimulation [8].…”