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

被引：5

作者：

Hsu, Cheng-Hsiung ^{[1
]}

Lin, Jian-Jhong ^{[1
]}

Yang, Tzi-Sheng ^{[2
]}

机构：

[1] Natl Cent Univ, Dept Math, Chungli 32001, Taiwan

[2] Tunghai Univ, Dept Math, Taichung 40704, Taiwan

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2015年 / 66卷 / 04期

关键词：

Multilayer cellular neural networks; Truncated technique; Weighted energy method; Comparison principle; LATTICE DYNAMICAL-SYSTEMS; ASYMPTOTIC SPEEDS; PROPAGATION; EQUATIONS; FAILURE; SPREAD; MODELS; FRONT;

D O I：

10.1007/s00033-014-0480-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：1355 / 1373

页数：19

共 36 条

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