Adaptive synchronization of uncertain time-delayed and multi-link network with arbitrary topology

We concentrate on the synchronization problem of the uncertain time-delayed network with multi-link. In this work, we design a novel technology to obtain the network synchronization condition so that we do not need to solve the Jacobi matrices of the state equations at the network nodes. Moreover, the uncertain parameters in state equations at the network nodes can also be identified simultaneously in the process of synchronization. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach. Our results are suitable for the multi-link network with arbitrary topology. And the dynamical network with single-link can be considered as a special case of dynamical network with multi-link.