On pinning control of some typical discrete-time dynamical networks

  • Zhang H
  • Li K
  • Fu X
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Recently, the pinning control of complex dynamical networks to their homogeneous states has been studied by many researchers, most of the dynamical networks are continuous-time ones, i.e., their dynamical behavior can be described by ODEs. An interesting result is that, for a continuous-time network, its desired (homogeneous) state can be achieved by pinning some nodes with relatively large degrees (also called the specifically pinning scheme [Wang XF, Chen GR. Pinning control of scale-free dynamical networks. Physica A 2002;310:521-31]). Is this specifically pinning scheme also effective for the discrete-time dynamical networks? In this paper, we demonstrate that the pinning control for a discrete-time dynamical network is difficult, and sometimes it is impossible to achieve the desired state just by controlling the nodes with larger degrees. In order to control the discrete-time dynamical networks successfully, we may need to control all the nodes. Finally, we also consider how to extend the interval for the feedback gain d for successful control. © 2009 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Complex network
  • Discrete-time
  • Homogenous state
  • Pinning control

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  • Haifeng Zhang

  • Kezan Li

  • Xinchu Fu

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