Synchronization of spatiotemporal networks via backstepping using neighbor information

A backstepping scheme is proposed for synchronization between two complex dynamical networks with different structures. The nodes of the networks are spatiotemporal chaotic systems. A recurrence relation containing the information from neighbors is established so that only one control input is needed to synchronize two spatiotemporal networks. The Lyapunov stability theory is applied to prove that the differences between the drive and response networks tend to zero asymptotically under the control. The proposed scheme is numerically implemented in the synchronization of two networks with the Fisher-Kolmogorov and the Burgers spatiotemporal chaotic systems as the nodes.