Cluster synchronisation of directed complex dynamical networks with nonidentical nodes via pinning control

In this article, we study the cluster synchronisation problem of directed complex dynamical networks through controlling some specific nodes. This method explains which nodes should be chosen as pinned candidates. Owing to the special structure of cluster network, the number of such nodes is extremely small. In our model, we consider a directed network whose nodes in different clusters are nonidentical. Then some sufficient conditions to guarantee cluster synchronisation in the coupled network are presented. Finally, numerical examples are given to verify our theoretical analysis.