Adaptive finite-time control for overlapping cluster synchronization in coupled complex networks

An overlapping cluster mathematical model is proposed.Several extended conditions are proposed to be appropriate not only for this model, but also for traditional cluster model.A novel control is designed for overlapping community networks to refine every inner cluster in overlapping clusters.An adaptive finite-time control is firstly proposed to force communities to achieve fast finite-time cluster synchronization. In this paper, we address the overlapping cluster synchronization problem of coupled complex networks via adaptive finite-time control. Cluster synchronization indeed has been extensively addressed by various control strategies. The communities in the cluster-based networks always do not share nodes with each other but exchange messages. Then, according to natural community, we propose a new overlapping community model for the coupled complex network to remove the restriction on common community models. The community in our model contains two kinds of nodes: overlapped and non-overlapped nodes, which is different from the common cluster form explored in the synchronization processing. In addition, a new control strategy is expressly proposed to extract every inner cluster in the overlapped regions. Especially, a novel adaptive finite-time control strategy is also proposed to force every community to a desired trajectory in finite time. On the basis of finite time theory, sufficient cluster synchronization criteria are derived. Lastly, the effectiveness of analytical results is confirmed by a numerical example.