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: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/490161 |
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| _version_ | 1832551676723068928 |
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| author | Zhi-Xian Yu Rong Yuan Cheng-Hsiung Hsu Ming-Shu Peng |
| author_facet | Zhi-Xian Yu Rong Yuan Cheng-Hsiung Hsu Ming-Shu Peng |
| author_sort | Zhi-Xian Yu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-6b1c94403be74a279ed66f97463ea5b2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6b1c94403be74a279ed66f97463ea5b22025-02-03T06:00:56ZengWileyAbstract 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 |
| 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 |
| title | 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_short | Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions |
| title_sort | traveling waves for delayed cellular neural networks with nonmonotonic output functions |
| url | http://dx.doi.org/10.1155/2014/490161 |
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