Topology identification for multi-layer complex dynamical networks with intra-layer coupling time delay

This paper investigates the topology identification of multi-layer complex dynamical network with intra-layer coupling time delay. The adaptive topology identification method with the same number of nodes in each layer is proposed. The original network is regarded as the drive network. For topology identification of the drive network, the response network with adaptive controller is constructed, the error dynamical network is also obtained. The Lyapunov stability theory and LaSalle’s invariant set principle are used to prove the asymptotic stability of the error dynamical network. Based on the adaptive controller, our approach can identify the topological structures of the complex dynamical networks. Finally, the numerical simulation is used to verify the effectiveness of the approach.