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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1355-1373
Number of pages	19
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	66
Issue number	4
DOIs	https://doi.org/10.1007/s00033-014-0480-z
State	Published - 10 Aug 2015

Keywords

Comparison principle
Multilayer cellular neural networks
Truncated technique
Weighted energy method

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abstract = "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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AU - Hsu, Cheng Hsiung

AU - Lin, Jian Jhong

AU - Yang, Tzi Sheng

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Y1 - 2015/8/10

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.

KW - Comparison principle

KW - Multilayer cellular neural networks

KW - Truncated technique

KW - Weighted energy method

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U2 - 10.1007/s00033-014-0480-z

DO - 10.1007/s00033-014-0480-z

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JF - Zeitschrift fur Angewandte Mathematik und Physik

IS - 4

ER -

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

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Keywords

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