Tempological Control of Network Dynamics

Abstract: Feedback control is an effective strategy for stabilizing a desired state and has been widely adopted in maintaining the stability of systems such as flying birds and power grids. By default, this framework requires continuous control input to offset deviations from the desired state, which can be invasive and cost a considerable amount of energy. Here, we introduce tempological (temporal + topological) control -- a novel, noninvasive strategy that harnesses the inherent flexibility of time-varying networks to control the dynamics of a general nonlinear system. By strategically switching network topology on-the-fly based on the current states of the nodes, we show how it is possible to drive a system to a desired state or even stabilize otherwise unstable states, all in the absence of external forcing. We demonstrate the utility of our approach using networks of Kuramoto and Stuart-Landau oscillators, achieving synchronization out of sets of unsynchronizable networks. Finally, we develop a statistical theory that explains why tempological control will almost always succeed in the limit of large and diverse temporal networks, with diversity of network configurations overcoming the deficiencies of any snapshot in isolation.