Brief paper: Pinning adaptive synchronization of a general complex dynamical network

  • Authors:

  • Jin Zhou;Jun-an Lu;Jinhu Lü

  • Affiliations:

  • College of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;College of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;LSC, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China and State Key Laboratory of Software Engineering, Wuhan University ...

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2008

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Abstract

There are two challenging fundamental questions in pinning control of complex networks: (i) How many nodes should a network with fixed network structure and coupling strength be pinned to reach network synchronization? (ii) How much coupling strength should a network with fixed network structure and pinning nodes be applied to realize network synchronization? To fix these two questions, we propose a general complex dynamical network model and then further investigate its pinning adaptive synchronization. Based on this model, we attain several novel adaptive synchronization criteria which indeed give the positive answers to these two questions. That is, we provide a simply approximate formula for estimating the detailed number of pinning nodes and the magnitude of the coupling strength for a given general complex dynamical network. Here, the coupling-configuration matrix and the inner-coupling matrix are not necessarily symmetric. Moreover, our pinning adaptive controllers are rather simple compared with some traditional controllers. A Barabasi-Albert network example is finally given to show the effectiveness of the proposed synchronization criteria.