Adaptive outer synchronization between two nonidentical networks using arbitrary coupling strength

In this paper, adaptive outer synchronization between two nonidentical networks using arbitrary coupling strength is investigated by the adaptive feedback controlling method. Based on Lyapunov stability theory, we prove that for networks with balanced structure topology, not only outer synchronization but also inner synchronization can be asymptotically reached by using arbitrary coupling strength. Then, the examples show that the coupling strength has great influence on the performance of outer synchronization for identical dynamical systems and nonidentical topology for a short time, but has little influence on the performance of outer synchronization for nonidentical dynamical systems and nonidentical topology. At last, we prove that this method can be also used for evolving complex networks.