Spatial Dynamics of Multilayer Cellular Neural Networks

Shi Liang Wu, Cheng Hsiung Hsu

Research output: Contribution to journalArticlepeer-review

Abstract

The purpose of this work is to study the spatial dynamics of one-dimensional multilayer cellular neural networks. We first establish the existence of rightward and leftward spreading speeds of the model. Then we show that the spreading speeds coincide with the minimum wave speeds of the traveling wave fronts in the right and left directions. Moreover, we obtain the asymptotic behavior of the traveling wave fronts when the wave speeds are positive and greater than the spreading speeds. According to the asymptotic behavior and using various kinds of comparison theorems, some front-like entire solutions are constructed by combining the rightward and leftward traveling wave fronts with different speeds and a spatially homogeneous solution of the model. Finally, various qualitative features of such entire solutions are investigated.

Original languageEnglish
Pages (from-to)3-41
Number of pages39
JournalJournal of Nonlinear Science
Volume28
Issue number1
DOIs
StatePublished - 1 Feb 2018

Keywords

  • Entire solution
  • Multilayer cellular neural network
  • Spreading speed
  • Traveling wave solution

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