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Mathematical Problems in Engineering
Volume 2018, Article ID 6384757, 11 pages
https://doi.org/10.1155/2018/6384757
Research Article

Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances

College of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China

Correspondence should be addressed to Junwei Sun; ten.haey@nusiewnuj

Received 29 September 2017; Revised 6 November 2017; Accepted 25 December 2017; Published 30 January 2018

Academic Editor: Yan-Wu Wang

Copyright © 2018 Jie Fang 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 studies the modified function projective synchronization of uncertain complex dynamic network model with multiple time-delay couplings and external disturbances. Based on Lyapunov stability theory, the positive definite function is designed and the sufficient conditions of synchronization are given. Both the uncertain parameters and the unknown bounded disturbances are estimated in accordance with the adaptive laws. With the adaptive feedback controller, the complex dynamic network can synchronize with reference node by a scaling function matrix. The reference node can be periodic orbit, equilibrium point, or a chaotic attractor. Finally, two numerical simulations are offered to illustrate the effectiveness of the proposed method.