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 | |
| State | Published - 2004 |
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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 journal › Article
}
TY - JOUR
T1 - Convergence and travelling fronts in functional differential equations with nonlocal terms
T2 - A competition model
AU - Gourley, Stephen A.
AU - Ruan, Shigui
PY - 2004
Y1 - 2004
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=2442624461&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=2442624461&partnerID=8YFLogxK
U2 - 10.1137/S003614100139991
DO - 10.1137/S003614100139991
M3 - Article
VL - 35
SP - 806
EP - 822
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 3
ER -