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Hybrid Adaptive Pinning Control for Function Projective Synchronization of Delayed Neural Networks with Mixed Uncertain Couplings

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  • T. Botmart
  • N. Yotha
  • P. Niamsup
  • W. Weera

Abstract

This paper presents the function projective synchronization problem of neural networks with mixed time-varying delays and uncertainties asymmetric coupling. The function projective synchronization of this model via hybrid adaptive pinning controls and hybrid adaptive controls, composed of nonlinear and adaptive linear feedback control, is further investigated in this study. Based on Lyapunov stability theory combined with the method of the adaptive control and pinning control, some novel and simple sufficient conditions are derived for the function projective synchronization problem of neural networks with mixed time-varying delays and uncertainties asymmetric coupling, and the derived results are less conservative. Particularly, the control method focuses on how to determine a set of pinned nodes with fixed coupling matrices and strength values and randomly select pinning nodes. Based on adaptive control technique, the parameter update law, and the technique of dealing with some integral terms, the control may be used to manipulate the scaling functions such that the drive system and response systems could be synchronized up to the desired scaling function. Finally, numerical examples are given to illustrate the effectiveness of the proposed theoretical results.

Suggested Citation

  • T. Botmart & N. Yotha & P. Niamsup & W. Weera, 2017. "Hybrid Adaptive Pinning Control for Function Projective Synchronization of Delayed Neural Networks with Mixed Uncertain Couplings," Complexity, Hindawi, vol. 2017, pages 1-18, August.
    • Handle: RePEc:hin:complx:4654020
    DOI: 10.1155/2017/4654020
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    1. Song, Qiang & Cao, Jinde & Liu, Fang, 2012. "Pinning synchronization of linearly coupled delayed neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 86(C), pages 39-51.
    2. Wang, Xiao Fan & Chen, Guanrong, 2002. "Pinning control of scale-free dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 521-531.
    3. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
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    Cited by:

    1. Lü, Ling & Wei, Qingtao, 2019. "Parameter estimation and synchronization in the uncertain financial network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).

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