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Decentralized adaptive pinning control for cluster synchronization of complex networks in the presence of delay-coupled and noise

This paper studies the pinning control for cluster synchronization of complex networks in the presence of coupling delay, and perturbation by noise. We propose a novel decentralized adaptive pinning control scheme for cluster synchronization of complex networks using a local adaptive strategy on both coupling strengths and feedback gains. The stochastic LaSalle invariance principle is employed to theoretically prove the almost certain synchronization of complex networks. An example is examined to illustrate the proposed synchronization scheme and demonstrate its effectiveness.