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

Abstract

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.

Keywords:

• cluster synchronisation
• directed complex dynamical networks
• delayed coupling
• nonidentical nodes
• pinning control

Acknowledgements

This project was supported by the State Key Program of National Natural Science of China (Grant No. 61134012), the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant 20090142110040 and the Fundamental Research Funds for the Central Universities, HUST: 2010MS001.