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Complexity
Volume 2017 (2017), Article ID 4654020, 18 pages
https://doi.org/10.1155/2017/4654020
Research Article

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

1Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
2Department of Applied Mathematics and Statistics, Rajamangala University of Technology Isan, Nakhon Ratchasima 30000, Thailand
3Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
4Department of Mathematics, University of Phayao, Phayao 56000, Thailand

Correspondence should be addressed to N. Yotha

Received 25 March 2017; Revised 14 June 2017; Accepted 2 July 2017; Published 8 August 2017

Academic Editor: Fathalla A. Rihan

Copyright © 2017 T. Botmart et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.