Synchronization of Dynamical Networks With Heterogeneous Delays via Time-Varying Pinning

This work investigates the synchronization problem of a dynamical network composed of nonlinear nodes with directed couplings and suffering from heterogeneous delays. Specifically, a time-varying pinning control is adopted to achieve synchronization. The system's dynamics are interpreted under a multiplex network framework, from which an indicator is designed to measure the synchronizability of the pinned network. Criteria are then derived to ensure exponential synchronization while the largest admissible coupling delay is also estimated. These criteria are based on the time average of the proposed indicator over some user-defined time intervals. Therefore, it possesses high versatility to support a wide range of scenarios with different intermittent control strategies. An interesting observation is that the proposed indicator is always upper bounded, manifesting that if the couplings between the nodes are too weak, pinning synchronization may fail no matter how large the pinning gain is. To further demonstrate the applicability of the theorem and the corollaries, numerical examples under different pinning configurations are presented.