Generalized lag synchronization of multiple weighted complex networks with and without time delay

The generalized lag synchronization of multiple weighted complex dynamical networks with fixed and adaptive couplings is investigated in this paper, respectively. By designing appropriate controller, several synchronization criteria are presented for multiple weighted complex dynamical networks with and without time delay based on the selected Lyapunov functional and inequality techniques. Moreover, an adaptive scheme to update the coupling weights is also developed for ensuring the generalized lag synchronization of multiple weighted complex dynamical networks with and without time delay. Finally, two numerical examples are provided in order to validate effectiveness of the proposed generalized lag synchronization criteria.