Existence and stability of traveling wave solutions for multilayer cellular neural networks

Cheng Hsiung Hsu; Jian Jhong Lin; Tzi Sheng Yang

doi:10.1007/s00033-014-0480-z

Existence and stability of traveling wave solutions for multilayer cellular neural networks

Cheng Hsiung Hsu, Jian Jhong Lin, Tzi Sheng Yang

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

5 引文斯高帕斯（Scopus）

摘要

The purpose of this article is to investigate the existence and stability of traveling wave solutions for one-dimensional multilayer cellular neural networks. We first establish the existence of traveling wave solutions using the truncated technique. Then we study the asymptotic behaviors of solutions for the Cauchy problem of the neural model. Applying two kinds of comparison principles and the weighed energy method, we show that all solutions of the Cauchy problem converge exponentially to the traveling wave solutions provided that the initial data belong to a suitable weighted space.

原文	???core.languages.en_GB???
頁（從 - 到）	1355-1373
頁數	19
期刊	Zeitschrift fur Angewandte Mathematik und Physik
卷	66
發行號	4
DOIs	https://doi.org/10.1007/s00033-014-0480-z
出版狀態	已出版 - 10 8月 2015

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10.1007/s00033-014-0480-z

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N2 - The purpose of this article is to investigate the existence and stability of traveling wave solutions for one-dimensional multilayer cellular neural networks. We first establish the existence of traveling wave solutions using the truncated technique. Then we study the asymptotic behaviors of solutions for the Cauchy problem of the neural model. Applying two kinds of comparison principles and the weighed energy method, we show that all solutions of the Cauchy problem converge exponentially to the traveling wave solutions provided that the initial data belong to a suitable weighted space.

AB - The purpose of this article is to investigate the existence and stability of traveling wave solutions for one-dimensional multilayer cellular neural networks. We first establish the existence of traveling wave solutions using the truncated technique. Then we study the asymptotic behaviors of solutions for the Cauchy problem of the neural model. Applying two kinds of comparison principles and the weighed energy method, we show that all solutions of the Cauchy problem converge exponentially to the traveling wave solutions provided that the initial data belong to a suitable weighted space.

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KW - Multilayer cellular neural networks

KW - Truncated technique

KW - Weighted energy method

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Existence and stability of traveling wave solutions for multilayer cellular neural networks

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