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

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. (C) 2017 Elsevier B.V. All rights reserved.