Abstract and Applied Analysis
Volume 2013 (2013), Article ID 402031, 12 pages
http://dx.doi.org/10.1155/2013/402031
Research Article

Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency

Xinsong Yang,1 Mengzhe Zhou,2 and Jinde Cao2,3

1Department of Mathematics, Chongqing Normal University, Chongqing 400047, China
2Department of Mathematics, Southeast University, Nanjing 210096, China
3Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 25 January 2013; Accepted 11 March 2013

Academic Editor: Qi Luo

Copyright © 2013 Xinsong Yang 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 investigates global synchronization in an array of coupled neural networks with time-varying delays and unbounded distributed delays. In the coupled neural networks, limited transmission efficiency between coupled nodes, which makes the model more practical, is considered. Based on a novel integral inequality and the Lyapunov functional method, sufficient synchronization criteria are derived. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using Matlab LMI Toolbox. It is displayed that, when some of the transmission efficiencies are limited, the dynamics of the synchronized state are different from those of the isolated node. Furthermore, the transmission efficiency and inner coupling matrices between nodes play important roles in the final synchronized state. The derivative of the time-varying delay can be any given value, and the time-varying delay can be unbounded. The outer-coupling matrices can be symmetric or asymmetric. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.