Entire solutions in lattice delayed differential equations with nonlocal interaction: Bistable cases

Z. C. Wang, W. T. Li, S. Ruan

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

This paper is concerned with entire solutions of a class of bistable delayed lattice differential equations with nonlocal interaction. Here an entire solution is meant by a solution defined for all (n,t) ×. Assuming that the equation has an increasing traveling wave front with nonzero wave speed and using a comparison argument, we obtain a two-dimensional manifold of entire solutions. In particular, it is shown that the traveling wave fronts are on the boundary of the manifold. Furthermore, uniqueness and stability of such entire solutions are studied.

Original languageEnglish (US)
Pages (from-to)78-103
Number of pages26
JournalMathematical Modelling of Natural Phenomena
Volume8
Issue number3
DOIs
StatePublished - 2013

Keywords

  • Bistable nonlinearity
  • Entire solution
  • Lattice delayed differential equation
  • Traveling wave front

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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