Pinning control of directed dynamical networks based on ControlRank

Abstract

By applying local feedback injections to a small fraction of network vertices, a dynamical network can be stabilized on a homogeneous equilibrium. However, different pinning strategies may lead to different performances. This paper develops a novel pinning scheme based on ControlRank (CR), which is a vertex centrality index exploring the link structure of the directed networks. Simulation study is given on a scale-free directed dynamical network, which demonstrates that it is much more effective to pin the vertex with largest CR than pin the vertex with largest out-degree.

Keywords:

• complex network
• directed graph
• scale-free
• ControlRank
• pinning control

AMS Subject Classification: :

• 34C28
• 34H05
• 94C15
• 60J20

Acknowledgements

We are grateful to Dr Xiang Li for his helpful comment, and thank Zhihai Rong, Xinbiao Lu, Lang Cao for useful discussions. This work was supported by the NSF of PRC under Grant No. 90412004, 70431002 and 60674045.