A variety of natural and man-made systems can be represented as complex networks with oscillatory activity of individual units. Examples can be found in biology, physics and engineering, from interacting neurons to power grids. Depending on the structure and the features of individual nodes, patterns may emerge in the whole network when all oscillators are in synchrony, or when they form synchronized groups or more complex partially synchronized configurations. Because the macroscopic function of a network is governed by such patterns, their stabilization or suppression is of relevance for applied problems, such as brain seizures or power grid blackouts. External intervention methods to manipulate oscillatory patterns have been proposed in the past, but improved control techniques to decrease computational cost and avoid outer network mediation, which is undesired in certain applications, still need further development.
In a recent work, Fabio Pasqualetti and colleagues introduced a method to prescribe the formation of desired patterns in networks of coupled oscillators through optimal interventions on the network structure. The authors used the network structural parameters as tuning instruments and showed that the emergence of prescribed synchronized patterns can be identified by solving convex optimization problems. Ultimately, this resulted in low computational complexity combined with minimal invasive interventions on the network. The authors also obtained algebraic and graph-theoretic conditions for the stability of target patterns, which ensured their robustness while taking into account the network’s structural constraints. The numerical verification of the method was performed for phase oscillators, and the authors also tested their approach with real-world examples of brain network and power grid. Interestingly, simulations of the network interventions associated with local metabolic changes induced the emergence of functional patterns of recorded neural activity in the brain network. When applied to a power distribution network, the method allowed the power flow to be restored after a fault. In addition to proposing an optimized way of network control by applying minimal interventions, the authors paved the way for the development of new techniques for more complex, sophisticated networked structures.
This is a preview of subscription content, access via your institution