Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions

Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions

This work investigates traveling waves for a class of delayed cellular neural networks with nonmonotonic output functions on the one-dimensional integer lattice Z. The dynamics of each given cell depends on itself and its nearest m left or l right neighborhood cells with distributed delay due to, fo...

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Main Authors: Zhi-Xian Yu, Rong Yuan, Cheng-Hsiung Hsu, Ming-Shu Peng
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/490161
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spelling doaj-6b1c94403be74a279ed66f97463ea5b22020-11-24T23:47:33ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/490161490161Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output FunctionsZhi-Xian Yu0Rong Yuan1Cheng-Hsiung Hsu2Ming-Shu Peng3College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaSchool of Mathematical Sciences, Beijing Normal University, Beijing 100875, ChinaDepartment of Mathematics, National Central University, Jhongli 32001, TaiwanDepartment of Mathematics, Beijing Jiaotong University, Beijing 100044, ChinaThis work investigates traveling waves for a class of delayed cellular neural networks with nonmonotonic output functions on the one-dimensional integer lattice Z. The dynamics of each given cell depends on itself and its nearest m left or l 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.http://dx.doi.org/10.1155/2014/490161
collection DOAJ
language English
format Article
sources DOAJ
author Zhi-Xian Yu
Rong Yuan
Cheng-Hsiung Hsu
Ming-Shu Peng
spellingShingle Zhi-Xian Yu
Rong Yuan
Cheng-Hsiung Hsu
Ming-Shu Peng
Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions
Abstract and Applied Analysis
author_facet Zhi-Xian Yu
Rong Yuan
Cheng-Hsiung Hsu
Ming-Shu Peng
author_sort Zhi-Xian Yu
title Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions
title_short Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions
title_full Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions
title_fullStr Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions
title_full_unstemmed Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions
title_sort traveling waves for delayed cellular neural networks with nonmonotonic output functions
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description This work investigates traveling waves for a class of delayed cellular neural networks with nonmonotonic output functions on the one-dimensional integer lattice Z. The dynamics of each given cell depends on itself and its nearest m left or l 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.
url http://dx.doi.org/10.1155/2014/490161
work_keys_str_mv AT zhixianyu travelingwavesfordelayedcellularneuralnetworkswithnonmonotonicoutputfunctions
AT rongyuan travelingwavesfordelayedcellularneuralnetworkswithnonmonotonicoutputfunctions
AT chenghsiunghsu travelingwavesfordelayedcellularneuralnetworkswithnonmonotonicoutputfunctions
AT mingshupeng travelingwavesfordelayedcellularneuralnetworkswithnonmonotonicoutputfunctions
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