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

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

Research output: Contribution to journalArticle

15 Citations (Scopus)

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

Fingerprint

Lattice Differential Equations
Delayed Differential Equation
Nonlocal Interactions
Entire Solution
Differential equations
Traveling Wavefronts
Wave Speed
Uniqueness

Keywords

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

ASJC Scopus subject areas

  • Modeling and Simulation

Cite this

Entire solutions in lattice delayed differential equations with nonlocal interaction : Bistable cases. / Wang, Z. C.; Li, W. T.; Ruan, Shigui.

In: Mathematical Modelling of Natural Phenomena, Vol. 8, No. 3, 2013, p. 78-103.

Research output: Contribution to journalArticle

@article{8745bd875b3d438a9eb00721ab411262,
title = "Entire solutions in lattice delayed differential equations with nonlocal interaction: Bistable cases",
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.",
keywords = "Bistable nonlinearity, Entire solution, Lattice delayed differential equation, Traveling wave front",
author = "Wang, {Z. C.} and Li, {W. T.} and Shigui Ruan",
year = "2013",
doi = "10.1051/mmnp/20138307",
language = "English (US)",
volume = "8",
pages = "78--103",
journal = "Mathematical Modelling of Natural Phenomena",
issn = "0973-5348",
publisher = "EDP Sciences",
number = "3",

}

TY - JOUR

T1 - Entire solutions in lattice delayed differential equations with nonlocal interaction

T2 - Bistable cases

AU - Wang, Z. C.

AU - Li, W. T.

AU - Ruan, Shigui

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Bistable nonlinearity

KW - Entire solution

KW - Lattice delayed differential equation

KW - Traveling wave front

UR - http://www.scopus.com/inward/record.url?scp=84879314113&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879314113&partnerID=8YFLogxK

U2 - 10.1051/mmnp/20138307

DO - 10.1051/mmnp/20138307

M3 - Article

AN - SCOPUS:84879314113

VL - 8

SP - 78

EP - 103

JO - Mathematical Modelling of Natural Phenomena

JF - Mathematical Modelling of Natural Phenomena

SN - 0973-5348

IS - 3

ER -