Journal of Applied Mathematics
Volume 2012 (2012), Article ID 689845, 12 pages
http://dx.doi.org/10.1155/2012/689845
Research Article

Fixed Point and Asymptotic Analysis of Cellular Neural Networks

Xianghong Lai1 and Yutian Zhang2

1School of Economics & Management, Nanjing University of Information Science & Technology, Nanjing 210044, China
2School of Mathematics & Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received 24 April 2012; Revised 16 July 2012; Accepted 2 August 2012

Academic Editor: Naseer Shahzad

Copyright © 2012 Xianghong Lai and Yutian Zhang. 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

We firstly employ the fixed point theory to study the stability of cellular neural networks without delays and with time-varying delays. Some novel and concise sufficient conditions are given to ensure the existence and uniqueness of solution and the asymptotic stability of trivial equilibrium at the same time. Moreover, these conditions are easily checked and do not require the differentiability of delays.