Synchronization of time-varying networks under fast switching

To understand the role of time-varying network topologies for stability of coupled systems, we examine sometimes-coupled oscillators where the network topology that describes oscillator coupling is time-varying. We show that if the network of oscillators synchronizes for the static time-average of the topology, then the network will synchronize with the time-varying topology if the time-average is achieved sufficiently fast. Although this sufficient condition appears to be very conservative, it provides new insights about the requirements for synchronization when the network topology is time-varying. In particular, it can be shown that networks of oscillators can synchronize even if at every point in time the frozen-time network topology is insufficiently connected to achieve synchronization