Outer-synchronization of complex networks with time-varying coupling delay

In this paper, synchronization between two networks, called outer synchronization for brevity, is theoretically and numerically studied. First, a sufficient criterion for this outer synchronization between two coupled networks with time-varying delay which have the same and different connection topologies is derived respectively. Numerical example is also given and it is in line with the theoretical analysis. Additionally, numerical investigations of two coupled networks which have different connection topologies are analyzed as well. The involved numerical result show that these coupled networks with different connection matrices can reach synchronization.