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

Stephen A. Gourley; Shigui Ruan

doi:10.1137/S003614100139991

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

Stephen A. Gourley, Shigui Ruan

Mathematics

Research output: Contribution to journal › Article › peer-review

106 Scopus citations

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 language	English (US)
Pages (from-to)	806-822
Number of pages	17
Journal	SIAM Journal on Mathematical Analysis
Volume	35
Issue number	3
DOIs	https://doi.org/10.1137/S003614100139991
State	Published - May 28 2004

Keywords

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

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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AU - Ruan, Shigui

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AB - 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.

KW - Competition-diffusion

KW - Energy function

KW - Equilibrium

KW - Geometric singular perturbation

KW - Stability

KW - Travelling front

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

Abstract

Keywords

ASJC Scopus subject areas

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