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

Cheng Hsiung Hsu, Jian Jhong Lin, Tzi Sheng Yang

Research output: Contribution to journalArticlepeer-review

4 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 languageEnglish
Pages (from-to)1355-1373
Number of pages19
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume66
Issue number4
DOIs
StatePublished - 10 Aug 2015

Keywords

  • Comparison principle
  • Multilayer cellular neural networks
  • Truncated technique
  • Weighted energy method

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