Convergence and travelling fronts in functional differential equations with nonlocal terms: A competition model

Stephen A. Gourley, Shigui Ruan

Research output: Contribution to journalArticle

96 Citations (Scopus)

Abstract

In this paper we consider a two-species competition model described by a reaction-diffusion system with nonlocal delays. In the case of a general domain, we study the stability of the equilibria of the system by using the energy function method. When the domain is one-dimensional and infinite, by employing linear chain techniques and geometric singular perturbation theory, we investigate the existence of travelling front solutions of the system.

Original languageEnglish (US)
Pages (from-to)806-822
Number of pages17
JournalSIAM Journal on Mathematical Analysis
Volume35
Issue number3
DOIs
StatePublished - 2004

Fingerprint

Travelling Fronts
Competition Model
Functional Differential Equations
Differential equations
Nonlocal Delay
Geometric Singular Perturbation Theory
Term
Reaction-diffusion System
Energy Function

Keywords

  • Competition-diffusion
  • Energy function
  • Equilibrium
  • Geometric singular perturbation
  • Stability
  • Travelling front

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics

Cite this

Convergence and travelling fronts in functional differential equations with nonlocal terms : A competition model. / Gourley, Stephen A.; Ruan, Shigui.

In: SIAM Journal on Mathematical Analysis, Vol. 35, No. 3, 2004, p. 806-822.

Research output: Contribution to journalArticle

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