Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 147164, 9 pages
Research Article

Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control

1Department of Mathematics, Chongqing Normal University, Chongqing 401331, China
2Department of Mathematics, Southeast University, Nanjing 210096, China
3Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 29 September 2012; Accepted 23 January 2013

Academic Editor: Sridhar Seshagiri

Copyright © 2013 Xinsong Yang and Jinde Cao. 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.


The drive-response synchronization of delayed neural networks with discontinuous activation functions is investigated via adaptive control. The synchronization of this paper means that the synchronization error approaches to zero for almost all time as time goes to infinity. The discontinuous activation functions are assumed to be monotone increasing which can be unbounded. Due to the mild condition on the discontinuous activations, adaptive control technique is utilized to control the response system. Under the framework of Filippov solution, by using Lyapunov function and chain rule of differential inclusion, rigorous proofs are given to show that adaptive control can realize complete synchronization of the considered model. The results of this paper are also applicable to continuous neural networks, since continuous function is a special case of discontinuous function. Numerical simulations verify the effectiveness of the theoretical results. Moreover, when there are parameter mismatches between drive and response neural networks with discontinuous activations, numerical example is also presented to demonstrate the complete synchronization by using discontinuous adaptive control.