Global synchronization in arrays of coupled networks with one single time-varying delay coupling

Global synchronization in arrays of coupled networks with one single time-varying delay coupling is investigated in this Letter. A general linear coupled network with a time-varying coupling delay is proposed and its global synchronization is further discussed. Some sufficient criteria are derived based on Lyapunov functional and linear matrix inequality (LMI). It is shown that under one single delay coupling, the synchronized state changes, which is different from the conventional synchronized solution. Moreover, the degree of the nodes and the inner delayed coupling matrix play key roles in the synchronized state. In particular, the derivative of the time-varying delay can be any given value. Finally, numerical simulations are given to illustrate the theoretical results.