Outer synchronization of coupled networks using arbitrary coupling strength

This paper mainly studies synchronization between two coupled networks, which is called "outer synchronization." On the basis of Lyapunov function approach, we prove that for networks with balanced structure topology, outer synchronization can be asymptotically reached by using arbitrary coupling strength. We employ a concept which arises in studying the average-consensus problem. Some numerical examples are presented to illustrate the result in the end. The examples indicate that the coupling strength has real influence on the performance of outer synchronization for a short time. The numerical examples also show that the transverse Lyapunov exponent is independent of the value of coupling strength.