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Abstract and Applied Analysis
Volume 2014, Article ID 490161, 11 pages
Research Article

Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions

1College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
3Department of Mathematics, National Central University, Jhongli 32001, Taiwan
4Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China

Received 13 April 2014; Accepted 25 June 2014; Published 22 July 2014

Academic Editor: Shengqiang Liu

Copyright © 2014 Zhi-Xian Yu 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.


This work investigates traveling waves for a class of delayed cellular neural networks with nonmonotonic output functions on the one-dimensional integer lattice . The dynamics of each given cell depends on itself and its nearest left or right neighborhood cells with distributed delay due to, for example, finite switching speed and finite velocity of signal transmission. Our technique is to construct two appropriate nondecreasing functions to squeeze the nonmonotonic output functions. Then we construct a suitable wave profiles set and derive the existence of traveling wave solutions by using Schauder's fixed point theorem.