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Science China Technological Sciences

, Volume 61, Issue 10, pp 1537–1545 | Cite as

Selecting pinning nodes to control complex networked systems

  • ZunShui Cheng
  • YouMing Xin
  • JinDe Cao
  • XingHuo Yu
  • GuoPing Lu
Article
  • 14 Downloads

Abstract

One of the fundamental problems in pinning control of complex networks is selecting appropriate pinning nodes, such that the whole system is controlled. This is particularly useful for complex networks with huge numbers of nodes. Recent research has yielded several pinning node selection strategies, which may be efficient. However, selecting a set of pinning nodes and identifying the nodes that should be selected first remain challenging problems. In this paper, we present a network control strategy based on left Perron vector. For directed networks where nodes have the same in- and out-degrees, there has so far been no effective pinning node selection strategy, but our method can find suitable nodes. Likewise, our method also performs well for undirected networks where the nodes have the same degree. In addition, we can derive the minimum set of pinning nodes and the order in which they should be selected for given coupling strengths. Our proofs of these results depend on the properties of non-negative matrices and M-matrices. Several examples show that this strategy can effectively select appropriate pinning nodes, and that it can achieve better results for both directed and undirected networks.

Keywords

complex network pinning control Perron root left Perron vector M-matrices 

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • ZunShui Cheng
    • 1
    • 2
    • 3
  • YouMing Xin
    • 1
  • JinDe Cao
    • 2
  • XingHuo Yu
    • 3
  • GuoPing Lu
    • 4
  1. 1.School of Mathematics and PhysicsQingdao University of Science and TechnologyQingdaoChina
  2. 2.Jiangsu Provincial Key Laboratory of Networked Collective Intelligence and School of MathematicsSoutheast UniversityNanjingChina
  3. 3.School of EngineeringRMIT UniversityMelbourneAustralia
  4. 4.School of Electrical EngineeringNantong UniversityNantongChina

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