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Mathematical Problems in Engineering
Volume 2015, Article ID 523424, 10 pages
http://dx.doi.org/10.1155/2015/523424
Research Article

Exponential Cluster Synchronization of Neural Networks with Proportional Delays

School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received 15 January 2015; Revised 9 March 2015; Accepted 24 March 2015

Academic Editor: Kun Liu

Copyright © 2015 Nian Feng 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

Exponential cluster synchronization of neural networks with proportional delays is studied in this paper. Unlike previous constant delay or bounded time delay, we consider the time-varying proportional delay is unbounded, less conservative, and more widely applied. Furthermore, we designed a novel adaptive controller based on Lyapunov function and inequality technique to achieve exponential cluster synchronization for neural networks and by using a unique way of equivalent system we proved the main conclusions. Finally, an example is given to illustrate the effectiveness of our proposed method.