Synchronizing network systems in the presence of limited resources via edge snapping

In this work, we propose a multilayer control protocol for the synchronization of network dynamical systems under limited resources. In addition to the layer where the interactions of the system take place, i.e., the backbone network, we propose a second, adaptive layer, where the edges are added or removed according to the edge snapping mechanism. Different from classic edge snapping, the inputs to the edge dynamics are modified to cap the number of edges that can be activated. After studying the local stability of the overall network dynamics, we illustrate the effectiveness of the approach on a network of Rossler oscillators and then show its robustness in a more general setting, exemplified with a model of the Italian high-voltage power grid.

Automated summary

In this work, a multilayer control protocol is proposed for achieving synchronization of network dynamical systems with limited resources. In addition to the backbone network where system interactions take place, a second adaptive layer is introduced with edge snapping mechanism to add or remove edges. The modified edge dynamics with capped number of activated edges are studied for local stability of the network dynamics. The effectiveness and robustness of the proposed approach are demonstrated on a network of Rossler oscillators and a model of the Italian high-voltage power grid.