Adaptive outer synchronization of delay-coupled nonidentical complex networks in the presence of intrinsic time delay and circumstance noise

This paper studies the outer synchronization of time delay complex networks of nonidentical topological structures in the presence of intrinsic time delay, time-varying coupling delay, and perturbation by noise. Considering one network as the drive network and the other as the response network, the drive-response networks achieve synchronization through a suitably designed adaptive controller. The stochastic LaSalle invariance principle is employed to theoretically prove the almost certain synchronization between two complex networks. The proposed controller is applicable to complex networks that have either intrinsic time delay or coupling delay or both. Two examples are examined to illustrate the proposed synchronization scheme and demonstrate its effectiveness.