Projective lag synchronization of the general complex dynamical networks with distinct nodes

In this paper, projective lag synchronization of the general complex dynamical networks with different nodes is investigated. Combining Barbalat’s lemma with adaptive control technique, the adaptive feedback controllers are constructed to achieve projective lag synchronization between the dynamical network with diverse nodes and arbitrary desired trajectory. The presented synchronization method can be applied to any complex networks. It is discovered that the update gains, the time delay, the network size and the network topology have influence on the synchronization effect. Furthermore, projective lag synchronization of the dynamical networks can still be efficiently realized in presence of noise and parameter perturbations. Corresponding numerical simulations are performed to validate the effectiveness and robustness of the proposed synchronization scheme.

► Projective lag synchronization of complex networks with distinct nodes is studied.
► The complex networks can be proportionally lag synchronized to any desired orbit.
► Increasing the update gains will accelerate the synchronization speed.
► The synchronization effect is affected by time delay, network size and topology.
► PLS can still be realized in presence of noise and parameter perturbations.