Traveling waves for nonlinear cellular neural networks with distributed delays

Zhi Xian Yu, Rong Yuan, Cheng Hsiung Hsu, Qin Jiang

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

In this paper, we will establish the existence and nonexistence of traveling waves for nonlinear cellular neural networks with finite or infinite distributed delays. The dynamics of each given cell depends on itself and its nearest m left or l right neighborhood cells where delays exist in self-feedback and left or right neighborhood interactions. Our approach is to use Schauder's fixed point theorem coupled with upper and lower solutions of the integral equation in a suitable Banach space. Further, we obtain the exponential asymptotic behavior in the negative infinity and the existence of traveling waves for the minimal wave speed by the limiting argument. Our results improve and cover some previous works.

Original languageEnglish
Pages (from-to)630-650
Number of pages21
JournalJournal of Differential Equations
Volume251
Issue number3
DOIs
StatePublished - 1 Aug 2011

Keywords

  • Cellular neural networks
  • Schauder's fixed point theorem
  • Traveling waves
  • Upper-lower solutions

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