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Pinning impulsive directed coupled delayed dynamical network and its applications

Author

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  • Chunnan Lin
  • Quanjun Wu
  • Lan Xiang
  • Jin Zhou

Abstract

The main objective of the present paper is to further investigate pinning synchronisation of a complex delayed dynamical network with directionally coupling by a single impulsive controller. By developing the analysis procedure of pinning impulsive stability for undirected coupled dynamical network previously, some simple yet general criteria of pinning impulsive synchronisation for such directed coupled network are derived analytically. It is shown that a single impulsive controller can always pin a given directed coupled network to a desired homogenous solution, including an equilibrium point, a periodic orbit, or a chaotic orbit. Subsequently, the theoretical results are illustrated by a directed small-world complex network which is a cellular neural network (CNN) and a directed scale-free complex network with the well-known Hodgkin–Huxley neuron oscillators. Numerical simulations are finally given to demonstrate the effectiveness of the proposed control methodology.

Suggested Citation

  • Chunnan Lin & Quanjun Wu & Lan Xiang & Jin Zhou, 2015. "Pinning impulsive directed coupled delayed dynamical network and its applications," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(2), pages 193-208, January.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:2:p:193-208
    DOI: 10.1080/00207721.2014.962646
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    References listed on IDEAS

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    1. Haibo Jiang & Jianjiang Yu & Caigen Zhou, 2011. "Consensus of multi-agent linear dynamic systems impulsive control protocols," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(6), pages 967-976.
    2. Guan Wang & Yi Shen, 2013. "Cluster synchronisation of directed complex dynamical networks with nonidentical nodes via pinning control," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(9), pages 1577-1586.
    3. Quanjun Wu & Jin Zhou & Lan Xiang, 2012. "Impulsive consensus seeking in directed networks of multi-agent systems with communication time delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(8), pages 1479-1491.
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    Cited by:

    1. Liu, Lingfeng & Liu, Kui & Xiang, Hongyue & Liu, Qian, 2020. "Pinning impulsive cluster synchronization of complex dynamical network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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